CHAPTER 28 THE CIRCLE AND ITS PROPERTIES
|
|
- Monica Leonard
- 7 years ago
- Views:
Transcription
1 CHAPTER 8 THE CIRCLE AND ITS PROPERTIES EXERCISE 118 Page Calculate the length of the circumference of a circle of radius 7. cm. Circumference, c = r = (7.) = 45.4 cm. If the diameter of a circle is 8.6 mm, calculate the circumference of the circle. Circumference, c = r = d = (8.6) = 59.5 mm. 3. Determine the radius of a circle whose circumference is 16.5 cm. Circumference, c = r from which, radius, r = c 16.5 = =.69 cm 4. Find the diameter of a circle whose perimeter is cm. If perimeter, or circumference, c = d, then = d and diameter, d = = cm 5. A crank mechanism is shown below, where XY is a tangent to the circle at point X. If the circle radius 0X is 10 cm and length 0Y is 40 cm, determine the length of the connecting rod XY. If XY is a tangent to the circle, then 0XY = , John Bird
2 Thus, by Pythagoras, 0Y = 0X + XY from which, XY = ( Y X ) = = = cm If the circumference of the Earth is km at the equator, calculate its diameter. Circumference, c = r = d from which, diameter, d = c = = 1 73 km = km, correct to 4 significant figures 7. Calculate the length of wire in the paper clip shown below. The dimensions are in millimetres. 1.5 Length of wire = (1.5) + ( ) + ( ) + ( ) = = = mm (3.5 3) ( ) , John Bird
3 EXERCISE 119 Page Convert to radians in terms of : (a) 30 (b) 75 (c) 5 (a) 30 = 30 rad = rad (b) 75 = 75 rad = 5 rad (c) 5 = 5 rad = rad = rad = 5 rad Convert to radians, correct to 3 decimal places: (a) 48 (b) 84 51' (c) 3 15' (a) 48 = 48 rad = rad 180 (b) = = rad = rad (c) 3 15 = 3.5 rad = rad Convert to degrees: (a) rad (b) rad (c) rad (a) 7 rad 6 (b) 4 rad 9 (c) 7 rad 1 = = 7 30 = 10 6 = = 4 0 = 80 9 = = 7 15 = Convert to degrees and minutes: (a) rad (b).69 rad (c) 7.41 rad (a) rad = = or , John Bird
4 (b).69 rad = = or (c) 7.41 rad = = or A car engine speed is 1000 rev/min. Convert this speed into rad/s rev/min = 1000 rev/min rad/rev 60s/min = rad/s , John Bird
5 EXERCISE 10 Page Calculate the area of a circle of radius 6.0 cm, correct to the nearest square centimetre. r = 6.0 = cm Area of circle = ( ). The diameter of a circle is 55.0 mm. Determine its area, correct to the nearest square millimetre. d 55.0 Area of circle = r = = 4 4 = 376 mm 3. The perimeter of a circle is 150 mm. Find its area, correct to the nearest square millimetre. Perimeter = circumference = 150 = r from which, radius, r = = 75 Area of circle = r = = 1790 mm 4. Find the area of the sector, correct to the nearest square millimetre, of a circle having a radius of 35 mm, with angle subtended at centre of 75. θ 75 = = 80 mm Area of sector = ( r ) ( 35 ) 5. An annulus has an outside diameter of 49.0 mm and an inside diameter of 15.0 mm. Find its area correct to 4 significant figures. d d = = = = 1709 mm Area of annulus = r 1 r ( d1 d ) ( ) 6. Find the area, correct to the nearest square metre, of a m wide path surrounding a circular plot of land 00 m in diameter , John Bird
6 = = 169 m 4 4 Area of path = ( d 1 d ) ( ) 7. A rectangular park measures 50 m by 40 m. A 3 m flower bed is made round the two longer sides and one short side. A circular fish pond of diameter 8.0 m is constructed in the centre of the park. It is planned to grass the remaining area. Find, correct to the nearest square metre, the area of grass. 8.0 Area of grass = (50 40) (50 3) (34 3) = = 1548 m 4 8. With reference to the diagram, determine (a) the perimeter and (b) the area. (a) Perimeter = ( 14) = cm (b) Area = (8 17) + ( 14 ) 1 = = cm 9. Find the area of the shaded portion shown. Shaded area = (10 10) (5) = = 1.46 m , John Bird
7 10. Find the length of an arc of a circle of radius 8.3 cm when the angle subtended at the centre is.14 radians. Calculate also the area of the minor sector formed. Arc length, s = rθ = (8.3)(.14) = cm 1 1 r θ = = m Area of minor sector = ( ) ( ) 11. If the angle subtended at the centre of a circle of diameter 8 mm is 1.46 rad, find the lengths of the (a) minor arc, and (b) major arc. If diameter d = 8 mm, radius r = 8 = 41 mm (a) Minor arc length, s = rθ = (41)(1.46) = mm (b) Major arc length = circumference minor arc = (41) = = mm 1. A pendulum of length 1.5 m swings through an angle of 10 in a single swing. Find, in centimetres, the length of the arc traced by the pendulum bob. Arc length of pendulum bob, s = rθ = (1.5) = 0.6 m or 6. cm 13. Determine the shaded area of the section shown , John Bird
8 Shaded area = (1 15) + 1 [(8) ] (5) = = = 0 mm 14. Determine the length of the radius and circumference of a circle if an arc length of 3.6 cm subtends an angle of 3.76 radians. s 3.6 Arc length, s = rθ from which, radius, r = θ = 3.76 = 8.67 cm Circumference = r = (8.67) = cm 15. Determine the angle of lap, in degrees and minutes, if 180 mm of a belt drive is in contact with a pulley of diameter 50 mm. Arc length, s = 180 mm, radius, r = 50 Since s = rθ, the angle of lap, θ = = 15 mm s 180 r = 15 = 1.44 rad = = Determine the number of complete revolutions a motorcycle wheel will make in travelling km, if the wheel s diameter is 85.1 cm. If wheel diameter = 85.1 cm, then circumference, c = d = (85.1) cm = cm =.6735 m Hence, number of revolutions of wheel in travelling 000 m = = Thus, number of complete revolutions = The floodlights at a sports ground spread its illumination over an angle of 40 to a distance of 48 m. Determine (a) the angle in radians and (b) the maximum area that is floodlit. (a) In radians, 40 = 40 rad = rad = rad, correct to 3 decimal places r θ = = 804. m (b) Maximum area floodlit = area of sector = ( ) ( ) , John Bird
9 18. Find the area swept out in 50 minutes by the minute hand of a large floral clock, if the hand is m long r = = m Area swept out = ( ) 19. Determine (a) the shaded area below and (b) the percentage of the whole sector that the area of the shaded area represents. 1 1 (a) Shaded area = (50) (0.75) (38) (0.75) 1 (0.75) = 396 mm = [ ] (b) Percentage of whole sector = (50) (0.75) 100% = 4.4% 0. Determine the length of steel strip required to make the clip shown. Angle of sector = = 30 = 30 rad = rad , John Bird
10 Thus, arc length, s = rθ = (15)(4.0146) = mm Length of steel strip in clip = = mm 1. A 50 tapered hole is checked with a 40 mm diameter ball as shown below. Determine the length shown as x. From the sketch below, tan 5 = 35 AC from which, AC = 35 tan 5 and sin 5 = 0 AB from which, AB = 0 sin 5 = mm = 47.3 mm i.e. AC = = x AB = x and x = i.e. x = 7.74 mm , John Bird
11 EXERCISE 11 Page Determine (a) the radius, and (b) the coordinates of the centre of the circle given by the equation: x + y 6x + 8y + 1 = 0 Method 1: The general equation of a circle ( x a) + ( y b) = r is x + y + ex + fy + c = 0 where coordinate a = e f, coordinate b = and radius r = a + b c Hence, if x + y 6x+ 8y+ 1 = 0 then a = e = 6 = 3, b = f 8 = = 4 (3) + ( 4) (1) = ( ) = 4 = and radius, r = [ ] i.e. the circle x + y 6x+ 8y+ 1 = 0 has (a) radius and (b) centre at (3, 4), as shown below. Method : x + y 6x+ 8y+ 1 = 0 may be rearranged as: ( x 3) + ( y+ 4) 4= 0 i.e. ( x 3) + ( y+ 4) = which has a radius of and centre at (3, 4). Sketch the circle given by the equation: x + y 6x + 4y 3 = 0 Method 1: The general equation of a circle ( x a) + ( y b) = r is x + y + ex + fy + c = 0 where coordinate a = e f, coordinate b = and radius r = a + b c Hence, if x + y 6x+ 4y 3= 0 then a = e = 6 = 3, b = f 4 = = and radius, r = [ ] (3) + ( ) ( 3) = ( ) = 16 = , John Bird
12 i.e. the circle x + y 6x+ 4y 3= 0 has centre at (3, ) and radius 4, as shown below. Method : x + y 6x+ 4y 3= 0 may be rearranged as: ( x 3) + ( y+ ) 16 = 0 i.e. ( x 3) + ( y+ ) = 4 which has a radius of 4 and centre at (3, ) 3. Sketch the curve: x + (y 1) 5 = 0 x + (y 1) 5 = 0 i.e. x + (y 1) = 5 i.e. x + (y 1) = 5 which represents a circle, centre (0, 1) and radius 5 as shown in the sketch below. 4. Sketch the curve: x = 6 y 1 6 If y x = then x y = and x y = , John Bird
13 i.e. x y + = 1 and x + y = which is a circle of radius 6 and co-ordinates of centre at (0, 0), as shown below , John Bird
14 EXERCISE 1 Page A pulley driving a belt has a diameter of 300 mm and is turning at 700/ revolutions per minute. Find the angular velocity of the pulley and the linear velocity of the belt, assuming that no slip occurs. Angular velocity, ω = n = = 90 rad/s Linear velocity v = ωr = (90) 3 = 13.5 m/s. A bicycle is travelling at 36 km/h and the diameter of the wheels of the bicycle is 500 mm, Determine the angular velocity of the wheels of the bicycle and the linear velocity of a point on the rim of one of the wheels Linear velocity, v = 36 km/h = m/s = 10 m/s 3600 (Note that changing from km/h to m/s involves dividing by 3.6) Radius of wheel, r = 500 = 50 mm = 0.5 m Since, v = ωr, then angular velocity, ω = v r = = 40 rad/s 3. A train is travelling at 108 km/h and has wheels of diameter 800 mm. (a) Determine the angular velocity of the wheels in both rad/s and rev/min. (b) If the speed remains constant for.70 km, determine the number of revolutions made by a wheel, assuming no slipping occurs. (a) Linear velocity, v = 108 km/h = Radius of wheel = 800 = 400 mm = 0.4 m Since, v = ωr, then angular velocity, ω = m/s = 30 m/s v 30 r = 0.4 = 75 rad/s , John Bird
15 rev 60s 75 rad/s = 75 rad/s = 716. rev/min rad min (b) Linear velocity, v = s t hence, time, t = s 700m v = 30 m/s = 90 s = = 1.5 minutes Since a wheel is rotating at 716. rev/min, then in 1.5 minutes it makes 716. rev/min 1.5 min = 1074 rev/min , John Bird
16 EXERCISE 13 Page Calculate the tension in a string when it is used to whirl a stone of mass 00 g round in a horizontal circle of radius 90 cm with a constant speed of 3 m/s. Tension in string = centripetal force = mv r 0.0 kg (3m/s) = = N 0.90m. Calculate the centripetal force acting on a vehicle of mass 1 tonne when travelling around a bend of radius 15 m at 40 km/h. If this force should not exceed 750 N, determine the reduction in speed of the vehicle to meet this requirement. Centripetal force = mv r velocity, v = 40 km/h = m/s Hence, centrifugal force = where mass, m = 1 tonne = 1000 kg, radius, r = 15 m and 40 (1000) If centrifugal force is limited to 750 N, then = 988 N (1000) v 750 = 15 from which, velocity, v = (750)(15) 1000 = m/s = = km/h Hence, reduction in speed is = 5.14 km/h 3. A speed-boat negotiates an S-bend consisting of two circular arcs of radii 100 m and 150 m. If the speed of the boat is constant at 34 km/h, determine the change in acceleration when leaving one arc and entering the other. Speed of the boat, v = 34 km/h = m/s , John Bird
17 For the first bend of radius 100 m, acceleration = v r = = 0.89 m/s 100 For the second bend of radius 150 m, acceleration = = = m/s, the negative sign indicating a change in direction Hence, change in acceleration is 0.89 ( 0.595) = 1.49 m/s , John Bird
CHAPTER 15 FORCE, MASS AND ACCELERATION
CHAPTER 5 FORCE, MASS AND ACCELERATION EXERCISE 83, Page 9. A car initially at rest accelerates uniformly to a speed of 55 km/h in 4 s. Determine the accelerating force required if the mass of the car
More informationAP Physics Circular Motion Practice Test B,B,B,A,D,D,C,B,D,B,E,E,E, 14. 6.6m/s, 0.4 N, 1.5 m, 6.3m/s, 15. 12.9 m/s, 22.9 m/s
AP Physics Circular Motion Practice Test B,B,B,A,D,D,C,B,D,B,E,E,E, 14. 6.6m/s, 0.4 N, 1.5 m, 6.3m/s, 15. 12.9 m/s, 22.9 m/s Answer the multiple choice questions (2 Points Each) on this sheet with capital
More informationTrigonometry LESSON ONE - Degrees and Radians Lesson Notes
210 180 = 7 6 Trigonometry Example 1 Define each term or phrase and draw a sample angle. Angle Definitions a) angle in standard position: Draw a standard position angle,. b) positive and negative angles:
More informationUnit 4 Practice Test: Rotational Motion
Unit 4 Practice Test: Rotational Motion Multiple Guess Identify the letter of the choice that best completes the statement or answers the question. 1. How would an angle in radians be converted to an angle
More information43 Perimeter and Area
43 Perimeter and Area Perimeters of figures are encountered in real life situations. For example, one might want to know what length of fence will enclose a rectangular field. In this section we will study
More informationCHAPTER 29 VOLUMES AND SURFACE AREAS OF COMMON SOLIDS
CHAPTER 9 VOLUMES AND SURFACE AREAS OF COMMON EXERCISE 14 Page 9 SOLIDS 1. Change a volume of 1 00 000 cm to cubic metres. 1m = 10 cm or 1cm = 10 6m 6 Hence, 1 00 000 cm = 1 00 000 10 6m = 1. m. Change
More informationChapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces. Copyright 2009 Pearson Education, Inc.
Chapter 5 Using Newton s Laws: Friction, Circular Motion, Drag Forces Units of Chapter 5 Applications of Newton s Laws Involving Friction Uniform Circular Motion Kinematics Dynamics of Uniform Circular
More informationChapter 3.8 & 6 Solutions
Chapter 3.8 & 6 Solutions P3.37. Prepare: We are asked to find period, speed and acceleration. Period and frequency are inverses according to Equation 3.26. To find speed we need to know the distance traveled
More informationCIRCUMFERENCE AND AREA OF A CIRCLE
CIRCUMFERENCE AND AREA OF A CIRCLE 1. AC and BD are two perpendicular diameters of a circle with centre O. If AC = 16 cm, calculate the area and perimeter of the shaded part. (Take = 3.14) 2. In the given
More informationENGINEERING COUNCIL DYNAMICS OF MECHANICAL SYSTEMS D225 TUTORIAL 1 LINEAR AND ANGULAR DISPLACEMENT, VELOCITY AND ACCELERATION
ENGINEERING COUNCIL DYNAMICS OF MECHANICAL SYSTEMS D225 TUTORIAL 1 LINEAR AND ANGULAR DISPLACEMENT, VELOCITY AND ACCELERATION This tutorial covers pre-requisite material and should be skipped if you are
More informationLesson 22. Circumference and Area of a Circle. Circumference. Chapter 2: Perimeter, Area & Volume. Radius and Diameter. Name of Lecturer: Mr. J.
Lesson 22 Chapter 2: Perimeter, Area & Volume Circumference and Area of a Circle Circumference The distance around the edge of a circle (or any curvy shape). It is a kind of perimeter. Radius and Diameter
More informationANALYTICAL METHODS FOR ENGINEERS
UNIT 1: Unit code: QCF Level: 4 Credit value: 15 ANALYTICAL METHODS FOR ENGINEERS A/601/1401 OUTCOME - TRIGONOMETRIC METHODS TUTORIAL 1 SINUSOIDAL FUNCTION Be able to analyse and model engineering situations
More information3 Work, Power and Energy
3 Work, Power and Energy At the end of this section you should be able to: a. describe potential energy as energy due to position and derive potential energy as mgh b. describe kinetic energy as energy
More informationPHY231 Section 2, Form A March 22, 2012. 1. Which one of the following statements concerning kinetic energy is true?
1. Which one of the following statements concerning kinetic energy is true? A) Kinetic energy can be measured in watts. B) Kinetic energy is always equal to the potential energy. C) Kinetic energy is always
More information16 Circles and Cylinders
16 Circles and Cylinders 16.1 Introduction to Circles In this section we consider the circle, looking at drawing circles and at the lines that split circles into different parts. A chord joins any two
More informationSOLID MECHANICS TUTORIAL MECHANISMS KINEMATICS - VELOCITY AND ACCELERATION DIAGRAMS
SOLID MECHANICS TUTORIAL MECHANISMS KINEMATICS - VELOCITY AND ACCELERATION DIAGRAMS This work covers elements of the syllabus for the Engineering Council exams C105 Mechanical and Structural Engineering
More informationPHY231 Section 1, Form B March 22, 2012
1. A car enters a horizontal, curved roadbed of radius 50 m. The coefficient of static friction between the tires and the roadbed is 0.20. What is the maximum speed with which the car can safely negotiate
More information3600 s 1 h. 24 h 1 day. 1 day
Week 7 homework IMPORTANT NOTE ABOUT WEBASSIGN: In the WebAssign versions of these problems, various details have been changed, so that the answers will come out differently. The method to find the solution
More informationwww.mathsbox.org.uk Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx Acceleration Velocity (v) Displacement x
Mechanics 2 : Revision Notes 1. Kinematics and variable acceleration Displacement (x) Velocity (v) Acceleration (a) x = f(t) differentiate v = dx differentiate a = dv = d2 x dt dt dt 2 Acceleration Velocity
More informationBy the end of this set of exercises, you should be able to:
BASIC GEOMETRIC PROPERTIES By the end of this set of exercises, you should be able to: find the area of a simple composite shape find the volume of a cube or a cuboid find the area and circumference of
More informationPHYSICS 111 HOMEWORK SOLUTION #9. April 5, 2013
PHYSICS 111 HOMEWORK SOLUTION #9 April 5, 2013 0.1 A potter s wheel moves uniformly from rest to an angular speed of 0.16 rev/s in 33 s. Find its angular acceleration in radians per second per second.
More informationAREA & CIRCUMFERENCE OF CIRCLES
Edexcel GCSE Mathematics (Linear) 1MA0 AREA & CIRCUMFERENCE OF CIRCLES Materials required for examination Ruler graduated in centimetres and millimetres, protractor, compasses, pen, HB pencil, eraser.
More informationUnit 1 - Radian and Degree Measure Classwork
Unit 1 - Radian and Degree Measure Classwork Definitions to know: Trigonometry triangle measurement Initial side, terminal side - starting and ending Position of the ray Standard position origin if the
More informationcircular motion & gravitation physics 111N
circular motion & gravitation physics 111N uniform circular motion an object moving around a circle at a constant rate must have an acceleration always perpendicular to the velocity (else the speed would
More informationChapter 10 Rotational Motion. Copyright 2009 Pearson Education, Inc.
Chapter 10 Rotational Motion Angular Quantities Units of Chapter 10 Vector Nature of Angular Quantities Constant Angular Acceleration Torque Rotational Dynamics; Torque and Rotational Inertia Solving Problems
More informationVOLUME AND SURFACE AREAS OF SOLIDS
VOLUME AND SURFACE AREAS OF SOLIDS Q.1. Find the total surface area and volume of a rectangular solid (cuboid) measuring 1 m by 50 cm by 0.5 m. 50 1 Ans. Length of cuboid l = 1 m, Breadth of cuboid, b
More informationPHYSICAL QUANTITIES AND UNITS
1 PHYSICAL QUANTITIES AND UNITS Introduction Physics is the study of matter, its motion and the interaction between matter. Physics involves analysis of physical quantities, the interaction between them
More informationPHYS 211 FINAL FALL 2004 Form A
1. Two boys with masses of 40 kg and 60 kg are holding onto either end of a 10 m long massless pole which is initially at rest and floating in still water. They pull themselves along the pole toward each
More informationObjective: To distinguish between degree and radian measure, and to solve problems using both.
CHAPTER 3 LESSON 1 Teacher s Guide Radian Measure AW 3.2 MP 4.1 Objective: To distinguish between degree and radian measure, and to solve problems using both. Prerequisites Define the following concepts.
More informationProblem Set 1. Ans: a = 1.74 m/s 2, t = 4.80 s
Problem Set 1 1.1 A bicyclist starts from rest and after traveling along a straight path a distance of 20 m reaches a speed of 30 km/h. Determine her constant acceleration. How long does it take her to
More informationPHYS 101-4M, Fall 2005 Exam #3. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
PHYS 101-4M, Fall 2005 Exam #3 Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 1) A bicycle wheel rotates uniformly through 2.0 revolutions in
More informationTeeJay Publishers General Homework for Book 3G Ch 9 - circles. Circles
Circles Homework Chapter 9 Exercise 1 1. For each of these circles, say whether the dotted line is a radius or a diameter :- (d) 2. Use two letters to name the line which is a diameter in this circle.
More informationSOLID MECHANICS DYNAMICS TUTORIAL MOMENT OF INERTIA. This work covers elements of the following syllabi.
SOLID MECHANICS DYNAMICS TUTOIAL MOMENT OF INETIA This work covers elements of the following syllabi. Parts of the Engineering Council Graduate Diploma Exam D5 Dynamics of Mechanical Systems Parts of the
More informationCentripetal Force. This result is independent of the size of r. A full circle has 2π rad, and 360 deg = 2π rad.
Centripetal Force 1 Introduction In classical mechanics, the dynamics of a point particle are described by Newton s 2nd law, F = m a, where F is the net force, m is the mass, and a is the acceleration.
More information226 Chapter 15: OSCILLATIONS
Chapter 15: OSCILLATIONS 1. In simple harmonic motion, the restoring force must be proportional to the: A. amplitude B. frequency C. velocity D. displacement E. displacement squared 2. An oscillatory motion
More informationWednesday 15 January 2014 Morning Time: 2 hours
Write your name here Surname Other names Pearson Edexcel Certificate Pearson Edexcel International GCSE Mathematics A Paper 4H Centre Number Wednesday 15 January 2014 Morning Time: 2 hours Candidate Number
More informationDownloaded from www.studiestoday.com
Class XI Physics Ch. 4: Motion in a Plane NCERT Solutions Page 85 Question 4.1: State, for each of the following physical quantities, if it is a scalar or a vector: Volume, mass, speed, acceleration, density,
More informationPHY121 #8 Midterm I 3.06.2013
PHY11 #8 Midterm I 3.06.013 AP Physics- Newton s Laws AP Exam Multiple Choice Questions #1 #4 1. When the frictionless system shown above is accelerated by an applied force of magnitude F, the tension
More informationUniform Circular Motion III. Homework: Assignment (1-35) Read 5.4, Do CONCEPT QUEST #(8), Do PROBS (20, 21) Ch. 5 + AP 1997 #2 (handout)
Double Date: Objective: Uniform Circular Motion II Uniform Circular Motion III Homework: Assignment (1-35) Read 5.4, Do CONCEPT QUEST #(8), Do PROBS (20, 21) Ch. 5 + AP 1997 #2 (handout) AP Physics B
More informationSection 6.1 Angle Measure
Section 6.1 Angle Measure An angle AOB consists of two rays R 1 and R 2 with a common vertex O (see the Figures below. We often interpret an angle as a rotation of the ray R 1 onto R 2. In this case, R
More information11. Rotation Translational Motion: Rotational Motion:
11. Rotation Translational Motion: Motion of the center of mass of an object from one position to another. All the motion discussed so far belongs to this category, except uniform circular motion. Rotational
More informationAll I Ever Wanted to Know About Circles
Parts of the Circle: All I Ever Wanted to Know About Circles 1. 2. 3. Important Circle Vocabulary: CIRCLE- the set off all points that are the distance from a given point called the CENTER- the given from
More informationTorque and Rotary Motion
Torque and Rotary Motion Name Partner Introduction Motion in a circle is a straight-forward extension of linear motion. According to the textbook, all you have to do is replace displacement, velocity,
More informationLinear Motion vs. Rotational Motion
Linear Motion vs. Rotational Motion Linear motion involves an object moving from one point to another in a straight line. Rotational motion involves an object rotating about an axis. Examples include a
More information9 Area, Perimeter and Volume
9 Area, Perimeter and Volume 9.1 2-D Shapes The following table gives the names of some 2-D shapes. In this section we will consider the properties of some of these shapes. Rectangle All angles are right
More informationGrade 7 Circumference
Grade 7 Circumference 7.SS.1 Demonstrate an understanding of circles by describing the relationships among radius, diameter, and circumference of circles relating circumference to PI determining the sum
More information11. Describing Angular or Circular Motion
11. Describing Angular or Circular Motion Introduction Examples of angular motion occur frequently. Examples include the rotation of a bicycle tire, a merry-go-round, a toy top, a food processor, a laboratory
More informationC B A T 3 T 2 T 1. 1. What is the magnitude of the force T 1? A) 37.5 N B) 75.0 N C) 113 N D) 157 N E) 192 N
Three boxes are connected by massless strings and are resting on a frictionless table. Each box has a mass of 15 kg, and the tension T 1 in the right string is accelerating the boxes to the right at a
More informationPhysics 1120: Simple Harmonic Motion Solutions
Questions: 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 Physics 1120: Simple Harmonic Motion Solutions 1. A 1.75 kg particle moves as function of time as follows: x = 4cos(1.33t+π/5) where distance is measured
More informationChapter 11. h = 5m. = mgh + 1 2 mv 2 + 1 2 Iω 2. E f. = E i. v = 4 3 g(h h) = 4 3 9.8m / s2 (8m 5m) = 6.26m / s. ω = v r = 6.
Chapter 11 11.7 A solid cylinder of radius 10cm and mass 1kg starts from rest and rolls without slipping a distance of 6m down a house roof that is inclined at 30 degrees (a) What is the angular speed
More informationPhysics 160 Biomechanics. Angular Kinematics
Physics 160 Biomechanics Angular Kinematics Questions to think about Why do batters slide their hands up the handle of the bat to lay down a bunt but not to drive the ball? Why might an athletic trainer
More informationF N A) 330 N 0.31 B) 310 N 0.33 C) 250 N 0.27 D) 290 N 0.30 E) 370 N 0.26
Physics 23 Exam 2 Spring 2010 Dr. Alward Page 1 1. A 250-N force is directed horizontally as shown to push a 29-kg box up an inclined plane at a constant speed. Determine the magnitude of the normal force,
More informationPhysics 201 Homework 8
Physics 201 Homework 8 Feb 27, 2013 1. A ceiling fan is turned on and a net torque of 1.8 N-m is applied to the blades. 8.2 rad/s 2 The blades have a total moment of inertia of 0.22 kg-m 2. What is the
More informationMechanical Principles
Unit 4: Mechanical Principles Unit code: F/60/450 QCF level: 5 Credit value: 5 OUTCOME 3 POWER TRANSMISSION TUTORIAL BELT DRIVES 3 Power Transmission Belt drives: flat and v-section belts; limiting coefficient
More informationHand Held Centripetal Force Kit
Hand Held Centripetal Force Kit PH110152 Experiment Guide Hand Held Centripetal Force Kit INTRODUCTION: This elegantly simple kit provides the necessary tools to discover properties of rotational dynamics.
More informationPendulum Force and Centripetal Acceleration
Pendulum Force and Centripetal Acceleration 1 Objectives 1. To calibrate and use a force probe and motion detector. 2. To understand centripetal acceleration. 3. To solve force problems involving centripetal
More informationExam 1 Review Questions PHY 2425 - Exam 1
Exam 1 Review Questions PHY 2425 - Exam 1 Exam 1H Rev Ques.doc - 1 - Section: 1 7 Topic: General Properties of Vectors Type: Conceptual 1 Given vector A, the vector 3 A A) has a magnitude 3 times that
More informationCHAPTER 6 WORK AND ENERGY
CHAPTER 6 WORK AND ENERGY CONCEPTUAL QUESTIONS. REASONING AND SOLUTION The work done by F in moving the box through a displacement s is W = ( F cos 0 ) s= Fs. The work done by F is W = ( F cos θ). s From
More informationDetermination of Acceleration due to Gravity
Experiment 2 24 Kuwait University Physics 105 Physics Department Determination of Acceleration due to Gravity Introduction In this experiment the acceleration due to gravity (g) is determined using two
More informationSOLUTIONS TO CONCEPTS CHAPTER 15
SOLUTIONS TO CONCEPTS CHAPTER 15 1. v = 40 cm/sec As velocity of a wave is constant location of maximum after 5 sec = 40 5 = 00 cm along negative x-axis. [(x / a) (t / T)]. Given y = Ae a) [A] = [M 0 L
More informationCandidate Number. General Certificate of Education Advanced Level Examination June 2014
entre Number andidate Number Surname Other Names andidate Signature General ertificate of Education dvanced Level Examination June 214 Physics PHY4/1 Unit 4 Fields and Further Mechanics Section Wednesday
More informationKINEMATICS OF PARTICLES RELATIVE MOTION WITH RESPECT TO TRANSLATING AXES
KINEMTICS OF PRTICLES RELTIVE MOTION WITH RESPECT TO TRNSLTING XES In the previous articles, we have described particle motion using coordinates with respect to fixed reference axes. The displacements,
More informationDeveloping Conceptual Understanding of Number. Set J: Perimeter and Area
Developing Conceptual Understanding of Number Set J: Perimeter and Area Carole Bilyk cbilyk@gov.mb.ca Wayne Watt wwatt@mts.net Perimeter and Area Vocabulary perimeter area centimetres right angle Notes
More informationNational Quali cations 2015
N5 X747/75/01 TUESDAY, 19 MAY 9:00 AM 10:00 AM FOR OFFICIAL USE National Quali cations 015 Mark Mathematics Paper 1 (Non-Calculator) *X7477501* Fill in these boxes and read what is printed below. Full
More informationAP Physics C. Oscillations/SHM Review Packet
AP Physics C Oscillations/SHM Review Packet 1. A 0.5 kg mass on a spring has a displacement as a function of time given by the equation x(t) = 0.8Cos(πt). Find the following: a. The time for one complete
More informationState Newton's second law of motion for a particle, defining carefully each term used.
5 Question 1. [Marks 20] An unmarked police car P is, travelling at the legal speed limit, v P, on a straight section of highway. At time t = 0, the police car is overtaken by a car C, which is speeding
More informationMCA Formula Review Packet
MCA Formula Review Packet 1 3 4 5 6 7 The MCA-II / BHS Math Plan Page 1 of 15 Copyright 005 by Claude Paradis 8 9 10 1 11 13 14 15 16 17 18 19 0 1 3 4 5 6 7 30 8 9 The MCA-II / BHS Math Plan Page of 15
More informationApplications for Triangles
Not drawn to scale Applications for Triangles 1. 36 in. 40 in. 33 in. 1188 in. 2 69 in. 2 138 in. 2 1440 in. 2 2. 188 in. 2 278 in. 2 322 in. 2 none of these Find the area of a parallelogram with the given
More informationAnswer, Key { Homework 6 { Rubin H Landau 1 This print-out should have 24 questions. Check that it is complete before leaving the printer. Also, multiple-choice questions may continue on the next column
More informationExperiment 9. The Pendulum
Experiment 9 The Pendulum 9.1 Objectives Investigate the functional dependence of the period (τ) 1 of a pendulum on its length (L), the mass of its bob (m), and the starting angle (θ 0 ). Use a pendulum
More informationMECHANICAL PRINCIPLES OUTCOME 4 MECHANICAL POWER TRANSMISSION TUTORIAL 1 SIMPLE MACHINES
MECHANICAL PRINCIPLES OUTCOME 4 MECHANICAL POWER TRANSMISSION TUTORIAL 1 SIMPLE MACHINES Simple machines: lifting devices e.g. lever systems, inclined plane, screw jack, pulley blocks, Weston differential
More informationRotation: Moment of Inertia and Torque
Rotation: Moment of Inertia and Torque Every time we push a door open or tighten a bolt using a wrench, we apply a force that results in a rotational motion about a fixed axis. Through experience we learn
More informationObjectives After completing this section, you should be able to:
Chapter 5 Section 1 Lesson Angle Measure Objectives After completing this section, you should be able to: Use the most common conventions to position and measure angles on the plane. Demonstrate an understanding
More informationChapter 6 Circular Motion
Chapter 6 Circular Motion 6.1 Introduction... 1 6.2 Cylindrical Coordinate System... 2 6.2.1 Unit Vectors... 3 6.2.2 Infinitesimal Line, Area, and Volume Elements in Cylindrical Coordinates... 4 Example
More informationD.3. Angles and Degree Measure. Review of Trigonometric Functions
APPENDIX D Precalculus Review D7 SECTION D. Review of Trigonometric Functions Angles and Degree Measure Radian Measure The Trigonometric Functions Evaluating Trigonometric Functions Solving Trigonometric
More informationAcceleration due to Gravity
Acceleration due to Gravity 1 Object To determine the acceleration due to gravity by different methods. 2 Apparatus Balance, ball bearing, clamps, electric timers, meter stick, paper strips, precision
More informationMechanical Principles
Unit 4: Mechanical Principles Unit code: F/601/1450 QCF level: 5 Credit value: 15 OUTCOME 4 POWER TRANSMISSION TUTORIAL 2 BALANCING 4. Dynamics of rotating systems Single and multi-link mechanisms: slider
More informationLecture Presentation Chapter 7 Rotational Motion
Lecture Presentation Chapter 7 Rotational Motion Suggested Videos for Chapter 7 Prelecture Videos Describing Rotational Motion Moment of Inertia and Center of Gravity Newton s Second Law for Rotation Class
More informationSOLID MECHANICS DYNAMICS TUTORIAL PULLEY DRIVE SYSTEMS. This work covers elements of the syllabus for the Edexcel module HNC/D Mechanical Principles.
SOLID MECHANICS DYNAMICS TUTORIAL PULLEY DRIVE SYSTEMS This work covers elements of the syllabus for the Edexcel module HNC/D Mechanical Principles. On completion of this tutorial you should be able to
More informationMidterm Solutions. mvr = ω f (I wheel + I bullet ) = ω f 2 MR2 + mr 2 ) ω f = v R. 1 + M 2m
Midterm Solutions I) A bullet of mass m moving at horizontal velocity v strikes and sticks to the rim of a wheel a solid disc) of mass M, radius R, anchored at its center but free to rotate i) Which of
More informationPaper Reference. Edexcel GCSE Mathematics (Linear) 1380 Paper 4 (Calculator) Friday 10 June 2011 Morning Time: 1 hour 45 minutes
Centre No. Candidate No. Paper Reference 1 3 8 0 4 H Paper Reference(s) 1380/4H Edexcel GCSE Mathematics (Linear) 1380 Paper 4 (Calculator) Higher Tier Friday 10 June 2011 Morning Time: 1 hour 45 minutes
More informationBiggar High School Mathematics Department. National 5 Learning Intentions & Success Criteria: Assessing My Progress
Biggar High School Mathematics Department National 5 Learning Intentions & Success Criteria: Assessing My Progress Expressions & Formulae Topic Learning Intention Success Criteria I understand this Approximation
More informationCircles - Past Edexcel Exam Questions
ircles - Past Edecel Eam Questions 1. The points A and B have coordinates (5,-1) and (13,11) respectivel. (a) find the coordinates of the mid-point of AB. [2] Given that AB is a diameter of the circle,
More informationCentripetal force, rotary motion, angular velocity, apparent force.
Related Topics Centripetal force, rotary motion, angular velocity, apparent force. Principle and Task A body with variable mass moves on a circular path with ad-justable radius and variable angular velocity.
More informationSupplemental Questions
Supplemental Questions The fastest of all fishes is the sailfish. If a sailfish accelerates at a rate of 14 (km/hr)/sec [fwd] for 4.7 s from its initial velocity of 42 km/h [fwd], what is its final velocity?
More informationAS COMPETITION PAPER 2008
AS COMPETITION PAPER 28 Name School Town & County Total Mark/5 Time Allowed: One hour Attempt as many questions as you can. Write your answers on this question paper. Marks allocated for each question
More informationSolution Derivations for Capa #11
Solution Derivations for Capa #11 1) A horizontal circular platform (M = 128.1 kg, r = 3.11 m) rotates about a frictionless vertical axle. A student (m = 68.3 kg) walks slowly from the rim of the platform
More informationPostulate 17 The area of a square is the square of the length of a. Postulate 18 If two figures are congruent, then they have the same.
Chapter 11: Areas of Plane Figures (page 422) 11-1: Areas of Rectangles (page 423) Rectangle Rectangular Region Area is measured in units. Postulate 17 The area of a square is the square of the length
More informationUNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level
UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS General Certificate of Education Ordinary Level *4274470357* MATHEMATICS (SYLLABUS D) 4024/11 Paper 1 October/November 2012 2 hours Candidates answer
More informationAngular acceleration α
Angular Acceleration Angular acceleration α measures how rapidly the angular velocity is changing: Slide 7-0 Linear and Circular Motion Compared Slide 7- Linear and Circular Kinematics Compared Slide 7-
More informationWhat You ll Learn. Why It s Important
What is a circle? Where do you see circles? What do you know about a circle? What might be useful to know about a circle? What You ll Learn Measure the radius, diameter, and circumference of a circle.
More informationPhysics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam
Physics 2A, Sec B00: Mechanics -- Winter 2011 Instructor: B. Grinstein Final Exam INSTRUCTIONS: Use a pencil #2 to fill your scantron. Write your code number and bubble it in under "EXAM NUMBER;" an entry
More informationGrade 7 & 8 Math Circles Circles, Circles, Circles March 19/20, 2013
Faculty of Mathematics Waterloo, Ontario N2L 3G Introduction Grade 7 & 8 Math Circles Circles, Circles, Circles March 9/20, 203 The circle is a very important shape. In fact of all shapes, the circle is
More informationSOLID MECHANICS BALANCING TUTORIAL BALANCING OF ROTATING BODIES
SOLID MECHANICS BALANCING TUTORIAL BALANCING OF ROTATING BODIES This work covers elements of the syllabus for the Edexcel module 21722P HNC/D Mechanical Principles OUTCOME 4. On completion of this tutorial
More informationCHAPTER 8, GEOMETRY. 4. A circular cylinder has a circumference of 33 in. Use 22 as the approximate value of π and find the radius of this cylinder.
TEST A CHAPTER 8, GEOMETRY 1. A rectangular plot of ground is to be enclosed with 180 yd of fencing. If the plot is twice as long as it is wide, what are its dimensions? 2. A 4 cm by 6 cm rectangle has
More informationAngular Velocity vs. Linear Velocity
MATH 7 Angular Velocity vs. Linear Velocity Dr. Neal, WKU Given an object with a fixed speed that is moving in a circle with a fixed ius, we can define the angular velocity of the object. That is, we can
More informationExamples of Scalar and Vector Quantities 1. Candidates should be able to : QUANTITY VECTOR SCALAR
Candidates should be able to : Examples of Scalar and Vector Quantities 1 QUANTITY VECTOR SCALAR Define scalar and vector quantities and give examples. Draw and use a vector triangle to determine the resultant
More informationPhysics 121 Sample Common Exam 3 NOTE: ANSWERS ARE ON PAGE 6. Instructions: 1. In the formula F = qvxb:
Physics 121 Sample Common Exam 3 NOTE: ANSWERS ARE ON PAGE 6 Signature Name (Print): 4 Digit ID: Section: Instructions: Answer all questions 24 multiple choice questions. You may need to do some calculation.
More informationUniversal Law of Gravitation
Universal Law of Gravitation Law: Every body exerts a force of attraction on every other body. This force called, gravity, is relatively weak and decreases rapidly with the distance separating the bodies
More information