1. PHYS 172: Modern Mechanics Lecture 16 – Multiparticle Systems, Moment of Inertia Read 9.3 – 9.5 Summer 2012

2. Rotational Kinetic Energy Consider a rigid system rotating on an axis All atoms are rotating at the same “angular speed”

3. Moment of Inertia

4. Some Moments of Inertia

5. Rigid Rotation about a Point Not the Center of Mass In General In this case What is K trans ?

7. Point particle system For both, real and point system: Point particle system: See derivation in the book

8. Application: Jumping up Point particle system: Real system: F N is pushing your feet which do not move! No work is done… Difference: point particle does not change shape

9. Application: Stretching a spring Point particle system: Real system: In real system: each force does work, involves displacement of the point to which the force is applied

10. Example: hockey pucks d1d1 d2d2

11. Example: a box containing a spring System: Ball with mass m ball Box with mass m box <<m ball Spring – massless M = m ball a b cm a) How fast will the ball move immediately after it sticks to a box? b) What is the increase in thermal energy of the ball? sticky assume Q=0 s

12. Clicker question 1 Wheel 1 of mass M rolls down from a slope. Wheel 2 of the same mass M slides down from the same slope (ignore friction) Which wheel will acquire larger total kinetic energy? A)Wheel 1 (rolling) B)Wheel 2 (sliding) C)The same 1 2

13. Clicker question 2 Wheel 1 of mass M rolls down from a slope. Wheel 2 of the same mass M slides down from the same slope (ignore friction) Which wheel will acquire larger translational kinetic energy? A)Wheel 1 (rolling) B)Wheel 2 (sliding) C)The same 1 2

14. Clicker question 3 Wheel 1 of mass M rolls down a slope. Wheel 2 of the same mass M slides down the same slope (ignore friction) Which of the wheels will get down first? A)Wheel 1 (rolling) B)Wheel 2 (sliding) C)Both will get down in the same time 1 2