Phys 221 exam 2 review

1. Phys 221 exam 2 review

2. Reminders: • NO SI THURSDAY!!

3. Exam Overview “Approximately 1/3 of the problems will stress understanding of the physics concepts, whereas the remainder will be numerical problems to test ability to apply these concepts.” -Syllabus 27 Questions

4. Statistical Breakdown of Exam 2 • 26% Energy • 17% Collisions (+Momentum) • 46% Rotational (Center of mass, moment of inertia, statics, angular momentum, torque) • 10% Gravitational Let’s put some analogies to work: Not knowing gravitation would be like losing 3 fingers Not knowing rotational is like losing a heart or both lungs

6. Energy • Conservation of Energy • Conservative/Non-conservative • Potential Energy • Springs • Collisions • Rotational • Gravitational Force/PE

7. KE • 2 types • Rotational • Translational

8. Springs • A 10 kg mass hits a spring at a speed of 50 m/s. The spring has k=30 N/m. • How far will the spring be compressed? • What will the PE of the spring be when it is fully compressed? • What will the PE of the spring be when it is halfway compressed?

9. Conservation of Energy • Find a method that works for you. • What’s most important is that you fully understand your method, front and back. • For me, I prefer doing one of two things: • If there’s no friction, I just write out the energy at the two points. • If there is friction, I use • =Work done by forces other than gravity

10. Define Mechanical Energy • KE • PE • KE+PE

11. Given a PE graph or function, what is F? • is just another symbol for • Where are the stable and unstable equilibriums? • At what points is the force zero? • At what points is the force negative? • Where does the particle have maximum speed, if it’s released at x=4?

12. Recall that at equilibriums, the force is zero. AKA You’re given • What is F at x=-2?

14. Conservative Forces vs. Non-conservative Forces • Conservative • Always associated with some PE • Work doesn’t depend on path taken • Examples: Gravity, Electrostatic • Not Conservative • PE doesn’t exist • Work does depend on path • Examples: Friction, Air resistance

15. Collisions • Momentum is a vector • Conservation of momentum • Impulse • Elastic, Inelastic, Completely Inelastic

16. Deciding elasticity

17. Is Momentum Conserved in a Collision • In this course, YES, ALWAYS!

19. Impulse • Impulse J: 3 ways to define • The impulse of A on B is equal and opposite to the impulse of B on A • A 5 kg ball hits a wall at 8 m/s and bounces back at the same speed. If the collision took 4 seconds, what is the average force done by the wall on the ball?

20. Rotational • Moment of Inertia=Rotational Inertia: • (about some axis) • Torque • (about some axis) • (about some axis) • Angular momentum • (about some axis) • Notice how everything angular is about some axis. Make sure that your choice of axes match. • Center of Mass!!

21. Center of Mass!! • Why is this important/grouped under rotation? =

22. Solve… • Mathematically… • Intuitively • Do circular or non-circular go faster down hills?

23. Angular momentum is the same for the two systems below about an axis through O.

24. Discrete/Continuous…which formula should I use? Discrete: Continuous: (use equation sheet for this) Discrete: Continuous:

25. Worked example What is the angular momentum?

26. Parallel Axis Theorem (PAT):

27. Torque ( • If net torque is zero, an object can still be moving. • In fact, the object can even be accelerating! • However, the angular acceleration must be zero, and the angular velocity must be constant.

28. Comparison between linear and angular Notice that there’s always an axis involved with every single rotational equivalent!

29. Statics • Can be solved in 2 minutes • Strategy: Generally, use conservation of angular momentum first!

31. Both discrete and continuous!

32. Is Momentum Conserved? • Is Angular Momentum Conserved?

33. Gravitation • Equation relating the period of a planet’s motion around a star of mass M • NOTE: r is the distance between the two masses, M is the mass of the object being orbited.

34. Examples: A planet is in a circular orbit around a star. The mass of the star is 5 * 1028 kg. If the period of the planet’s orbit is 1.00 * 105 s, then the orbital radius of the planet around the star is ____ m. The centers of two small uniform spherical bodies are separated by a distance d and the magnitude of the attractive gravitational force of one on the other is F. If the distance between the centers of the bodies decreases to d/2, the magnitude of the force of one on the other becomes ____ .

36. A 1.53-kg mass hangs on a rope wrapped around a disk pulley of mass 7.07 kg and radius 66.0 cm. The rope does not slip on the pulley. • What is the angular acceleration of the pulley? • If the block has fallen 0.8 m, what is the speed of the block at that time? (Two ways to solve this)

37. Other Concepts • Magnitude of Forces, vectors, etc…

38. Multi-Principle Problems A

39. Trickier Problems