Page 1 of 10. Answer: 1 rad = 57.3 o

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1 Page 1 of 10 CTot-1. How many degrees in 1 radian? A) 1 rad = 2 degrees B) 1 rad = 180 o C) 1 rad = 10 o D) 1 rad = 57.3 o E) adian is not a measure of angle, so the question makes no sense. Answer: 1 rad = 57.3 o CTot-2. A pocket watch and Big Ben are both keeping perfect time. Which minute hand has the larger magnitude angular velocity? A) Pocket watch's B) Big Ben's C) Same on both. Which minute hand's tip has the larger magnitude tangential velocity? A) Pocket watch's B) Big Ben's C) Same v on both. pocket watch Big Ben Answer: Both have the same = 2 rad/3600 s. The minute hand of Big Ben has the larger tangential speed, since v = r. CTot-3. A small wheel and a large wheel are connected by a belt. The small wheel is turned at a constant angular velocity S. How does the magnitude of the angular velocity of the large wheel L compare to that of the small wheel? s L A) s = L B) s > L C) s < L There is a bug S on the rim of the small wheel and another bug L on the rim of the large wheel. How do their speeds compare? A) S = L B) S > L C) S < L Answers: s > L The speeds are the same: S = L

2 Page 2 of 10 CTot-4. A student sees the following question on an exam: A flywheel with mass M= 120 kg, and radius r = 0.6 m, starting at rest, has an angular acceleration of = 0.1 rad/s 2. How many revolutions has the wheel undergone after 10 s? Which formula should the student use to answer the question? A) t 0 B) t t C) 2 ( ) Answer: B CTot-5. A student in Physics 1110 sees the following question on CAPA Q#2 due the following Friday night. An engine flywheel turns with constant angular speed of 100 rev/min. When the engine is shut off, friction slows the wheel to rest in 2 hours. What is the magnitude of the constant angular acceleration of the wheel? Give the answer in units of rev/min 2. The student writes f 2 (100 rev/min), so t t t 120 min Does the answer come out correctly with the desired units of rev/min 2? A) Yes B) No Answer: No! This calculation gives the answer in units of rad/min 2. The factor of 2 has units of rad/rev.

3 Page 3 of 10 CTot-6. A ladybug is clinging to the rim of a spinning wheel which is spinning CCW and is speeding up. At the moment shown, when the bug is at the far right, what is the approximate direction of the ladybug's acceleration? A) B) C) D) E) Answer: Draw the v1-v2- v diagram. CTot-7. What is the magnitude of the angular acceleration of a spinning wheel that is spinning at constant rate? A) zero B) v 2 / C) g D) 2 /T E) None of these Answer: = constant means that = 0. CTot-8. Three forces labeled A, B, C are applied to a rod which pivots on an axis thru its 0 0 center. [ cos(45 ) sin(45 ) 1/ ]. Which force causes the largest magnitude torque? A B C D) two or more forces tie for largest size torque. A F 45 o B /2 F C axis 2F /4 Answer: A has the largest magnitude torque

4 Page 4 of 10 CTot-9. Three forces are applied to a rod which rotates about the center. What is the net torque about the axis? ecall the sign convention F F axis /2 A) +F B) F C) zero D) +3F E) 3F 2F Answer: zero CTot-10. A mass is hanging from the end of a horizontal bar which pivots about an axis through it center, but it being held stationary. The bar is released and begins to rotate. As the bar rotates from horizontal to vertical, the magnitude of the torque on the bar.. A) increases B) decreases C) remains constant As the bar rotates from horizontal to vertical, the magnitude of the angular acceleration of the bar.. A) increases B) decreases C) remains constant Answers: The torque decreases and also decreases. The angular velocity increases in magnitude.

5 Page 5 of 10 CTot-11. A light rod of length 2L has 2 small heavy masses (each with mass m) attached at the end and the middle. The axis of rotation is at one end, as shown. What is the moment of inertia about the axis? L L axis m m A) 2 m L 2 B) 4 m L 2 C) 5 m L 2 D) 8 m L 2 E) None of these What is the magnitude of the net torque due to gravity? A) 2mgL B) 3mgL C) 4mgL D) 5mgL If the bar is released from rest what is the magnitude of the initial angular acceleration? A) 3g/(5L) B) 5g/(3L) C) 7L/(3g) D) 3L/(5g) Answers: I = 5 m L 2, = 3mgL, = / I = 3g/(5L) CTot-12. A mallet consists of a heavy steel cubical head on a light wooden handle. About which axis of rotation is the moment of inertia I a maximum? A B C D Answer: B

6 Page 6 of 10 CTot-13. Consider a rod of uniform density with an axis of rotation through its center and an identical rod with the axis of rotation through one end. Which has the larger moment of inertia? C E axis axis A) I C > I E B ) I C < I E C ) I C = I E Answer: I C < I E CTot-14. Two wheels, each with the same radius and the same total mass M, are rotating about their fixed axels. Wheel A is a hoop with all the mass very near the rim. Wheel B is a disk with the mass spread out uniformly. Which has the larger moment-of-inertia I = m i r i 2? A) Hoop B) Disk C) both have the same I hoop disk M, M, Answer: The hoop has larger moment-of-inertia.

7 Page 7 of 10 CTot-15. A mass m hangs from string wrapped around a pulley of radius. The pulley has a moment of inertia I and its pivot is frictionless. Because of gravity, the mass accelerates downward and the pulley rotates. Which has greater magnitude, the string tension F T or the weight mg? A) F T = mg B) F T < mg C) F T > mg The magnitude of the torque on the pulley is.. A) greater than mg B) less than mg C) equal to mg Answers: F T < mg (Since the mass is accelerating downward, the downward force must be greater than the upward force. ) The magnitude of the torque on the pulley is F T which is less than mg (since F T < mg ) m a CTot-16. A sphere, a hoop, and a cylinder, all with the same mass M and same radius, are rolling along, all with the same speed v. Which has the most total kinetic energy? A) Sphere B) Hoop C) Disk D) All have the same KE. Sphere Hoop Disk v v v Answer: Hoop. All have the same KE trans, but the hoop has the most KE rot, so it has the greatest KE tot = KE trans +KE rot.

8 Page 8 of 10 CTot-17. Two hoops, A and B, both with the same mass M, are each rotating about an axis thru the center. Hoop B has twice the diameter (twice the ) and is rotating at twice the rate (twice the ) as hoop A. What is the ration KE B / KE A? A B 2 A) 2 B) 4 C) 6 D) 8 E) 16 Answer: 16. KE rot = (1/2) I 2 and I hoop = M 2, so there is a factor of 4 due to I, and another factor of 4 due to. CTot-18. A disk and a hoop, both with the same mass M and the same radius, both start from rest at the top and roll down an incline. Which one has the largest total kinetic energy at the bottom? A) Disk B) Hoop C) same KE tot for both Answer: same KE tot for both (since they start out with the same PE grav = Mgh) CTot-19. A disk and a hoop, both with the same mass M and the same radius, both roll without slipping with the same speed v, and are rolling toward an inclined plane, as shown. Which object will roll up to the greatest height on the incline? A) Disk B) Hoop C) same max height for both v v Answer: Hoop has more total KE so it will roll to the greatest height.

9 Page 9 of 10 CTot-20. Two light (massless) rods, labeled A and B, each are connected to the ceiling by a frictionless pivot. od A has length L and has a mass m at the end of the rod. od B has length L/2 and has a mass 2m at its end. Both rods are released from rest in a horizontal position. L A L/2 B 2m Which one experiences the larger torque? A) A B) B C) Both have the same size. Which one has the largest moment of inertia I (about the pivot)? A) A B) B C) Both have the same size I Which one falls to the vertical position fastest? A) A B) B C) Both fall at the same rate. (Hint: I ) m Answers: torques are the same. A has the larger I. B fall the fastest, since it has the largest.

10 Page 10 of 10 CTot-21. Two wheels with fixed axles, each have the same mass M, but wheel 2 has twice the radius of wheel 1. Each is accelerated from rest with a force applied as shown. Assume that all the mass of the wheels is concentrated in the rims so that the moment of inertia of each is of the form I = M 2 (hoop formula). In order to impart identical angular accelerations to both wheels, how much larger is F 2 than F 1? ecall that I. F 1 F 2 Wheel 1, radius, mass M 2 Wheel 2, radius 2, mass M A) F 2 = F 1. B) F 2 = 2F 1. C) F 2 = 4F 1. D) F 2 = 8F 1. E) None of these. Answer: Don't try to do this in your head. Set up the ratio 2 / 1 = (2F 2 )/(F 1 ) = I 2 /I 1 = I 2 /I 1. You will find F 2 = 2F 1. CTot-22. A mass m is attached to a long, massless rod. The mass is close to one end of the rod. Is it easier to balance the rod on end with the mass near the top or near the bottom? Hint: Small means sluggish behavior and A) easier with mass near top. B) easier with mass near bottom. C) No difference.. I Answer: easier with mass near top. If the length of the rod is L, then L, I L 2 and so 1/L. Longer L means smaller, more sluggish motion, easier to balance. mg m

PHYSICS 111 HOMEWORK SOLUTION #10. April 8, 2013

PHYSICS 111 HOMEWORK SOLUTION #10. April 8, 2013 PHYSICS HOMEWORK SOLUTION #0 April 8, 203 0. Find the net torque on the wheel in the figure below about the axle through O, taking a = 6.0 cm and b = 30.0 cm. A torque that s produced by a force can be