Energy and Angular Momentum. Laws of Conservation.

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Gerald Bond
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1 Energy and Angular Momentum. Laws of Conservation.

2 Announcements n Homework # 2 is due on Friday, Oct. 7 th. n First in-class exam will take place on Thursday, October 6th. Please, remember your STUDENT ID!!! (no ID no Exam) Please remember to bring a pencil # 2. List of Textbook Units for Exam 1 are on the course website ( under the link `Exams Homework # 2 offers good practice for the exam!

3 n Unit 20 Assigned Reading

4 Today s Goals 1) To introduce the concept of energy and energy conservation. 2) To introduce the concept of angular momentum, and angular momentum conservation.

5 Energy and Energy Conservation

6 What is Energy? n It is the amount of total work an object (or you) does or can do. You need a good breakfast to store enough energy for a good day of learning (work) If we lift a rock from the ground, we `work against gravity, and we store that `energy in the rock (potential energy). That stored energy is released when we let the rock go, and the rock falls to the ground (kinetic [movement] energy); when the rock impacts the ground, the kinetic energy is `dissipated in thermal (heat) energy

7 Energy comes in different forms. n Kinetic Energy Bulk motion (the motion of a body) Thermal Energy (Heat) n Potential Energy (will be explained soon!) Gravitational potential energy Mechanical potential energy Electromagnetic potential energy n Radiative Energy We ll spend at least one entire class on this one.

8 Energy is measured in Joules n A Joule (J) is an amount of energy. n Power is the rate of energy usage. Power is measured in Watts (W) and is the number of Joules used in one second. 1 W = 1 J/s (one horsepower = 745 W)

9 New energy is never created! n All forms of energy on Earth and in the Universe can be traced back to an earlier incarnation of energy. Why do sweet fruits generally grow in the south?

10 Energy can change form, but is never created or destroyed! Energy is conserved! one form of energy Another form

11 Kinetic Energy n Kinetic energy is always due to some kind of motion. Objects at rest have no kinetic energy (KE=0). You can calculate an objects kinetic energy by knowing its mass and velocity. KE = 1/2 mv 2 mass Velocity squared This is energy so it s measured in Joules!

12 KE = 1/2 mv 2 Large mass, small velocity small mass, large velocity A 10 gram bullet moving at 700m/s and a 500kg rock rolling at 3m/s have roughly the same amount of kinetic energy!

13 Survey Question KE = 1/2 mv 2 Which one of the following has the greatest kinetic energy? 1) a 1 kg soccer ball moving at 4 m/s 2) a 100 kg anvil that is stationary 3) a 4 kg soccer ball moving at 2 m/s 4) a 5 kg soccer ball moving at 1 m/s 5) a 2 kg soccer ball moving at 3 m/s

14 Watch out for fast things! n Damage in a car crash is proportional to v 2. n Trauma to head from falling anvil is proportional to v 2 (or equivalently to how high it started from) n A hurricane with 120 m.p.h. winds packs four times the punch of a tropical storm with 60 m.p.h. winds.

15 Thermal Energy n Thermal energy is another form of kinetic energy (it is the motion of the atoms/ molecules in the object s material) n It is the lowest form of energy n A hot object has more thermal energy than a cold object

16 Survey Question The most energy inefficient thing you can do while driving (assuming you are moving) is 1) to use your momentum to coast up a hill 2) to have your headlights on 3) to run your air conditioner 4) to apply the brakes 5) to accelerate rapidly

17 Potential Energy n What is Potential Energy? It is the total amount of stored work an object (or you) can potentially do. A rock held in your hand above the ground is storing gravitational potential energy. If you let the rock go, the potential energy is released in kinetic energy. n Potential energy comes in different forms: Gravitational potential energy (perched on a cliff) Chemical potential energy (e.g., a battery) Nuclear potential energy (stored in the nuclei of atoms) Mechanical potential energy (like a compressed spring) Electromagnetic potential energy (like when you hold two magnets close to each other)

18 Gravitational Potential Energy n All objects with mass attract each other due to their gravitational force. Associated with this force is a gravitational potential energy: Newton s constant E grav = G M 1 M 2 d n For an object near the surface of the Earth: E grav = mgh distance between objects The object s mass The object s height The acceleration due to gravity near the surface of the Earth: g=9.8 m/s 2

19 Kinetic and Potential Energy n Kinetic energy is associated with motion; a ball in motion will have kinetic energy: KE = ½ m v 2 which can be derived by measuring its mass and velocity. n Potential energy is energy stored (e.g., water behind a dam, a ball at the edge of a table, etc.); if the ball rolls out of the table, the potential energy is converted to kinetic energy. Gravitational potential energy is: E g = GMm/R

20 Angular Momentum and Its Conservation

21 Angular Momentum n It is the `quantity of motion of a spinning (rotating) object. L = m. v. r = P. r (units: kg m 2 s -1 ) n Depends on the geometry, the mass, and the rotational velocity of an object. n Angular momentum is conserved. A spinning wheel wants to keep spinning. A stationary wheel wants to keep still. Conservation is the tendency of a spinning object to keep spinning with the rotation axis in a constant direction n Angular momentum is also a vector quantity this means that the direction of the axis of rotation is significant and resistant to change.

22 Everyday Examples of the Conservation of Angular Momentum n Riding a bike n Spinning a basketball on your finger n Steering a satellite n A spinning ice skater

23 Figuring out orbital velocities with angular momentum n The angular momentum of an object (like a planet) moving in a circle (like an orbit!) is: L = m v r = constant v m = mass of planet v = velocity of planet r = orbital radius of planet m r

24 Kepler s Second Law of Orbits 2. As a planet moves around it s orbit, the closer the planet to the Sun, the higher its speed. 1 month

25 How to think about the conservation of angular momentum. The angular momentum before is equal to the angular momentum afterwards. For a planet or satellite: Angular Momentum when close Angular Momentum when distant L 1 = m 1 v 1 r 1 L 2 = m 2 v 2 r 2 but L 1 = L 2 Since m 1 =m 2, v 1 r 1 = v 2 r 2 This is Kepler s Second Law

26 Survey Question L = m v r If Earth orbited the Sun at a distance of ½ AU but with the same angular momentum that it now has, how much faster/slower would its orbital velocity be? 1) ¼ its current value 2) ½ its current value 3) the same as its current value 4) 2 times its current value 5) 4 times its current value

In science, energy is the ability to do work. Work is done when a force causes an

What is energy? In science, energy is the ability to do work. Work is done when a force causes an object to move in the direction of the force. Energy is expressed in units of joules (J). A joule is calculated