PHYS 172 Modern Mechanics Lecture 16 Multiparticle Systems

PHYS 172: Modern Mechanics Lecture 16 – Multiparticle Systems, Moment of Inertia Summer 2012 Read 9. 3 – 9. 5

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

Moment of Inertia

Some Moments of Inertia

Rigid Rotation about a Point Not the Center of Mass In General In this case What is Ktrans?

What is Ktrans?

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

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

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

Example: hockey pucks d 1 d 2

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

Clicker question 1 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? 2 A) Wheel 1 (rolling) B) Wheel 2 (sliding) C) The same

Clicker question 2 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 translational kinetic energy? 2 A) Wheel 1 (rolling) B) Wheel 2 (sliding) C) The same

Clicker question 3 1 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? 2 A) Wheel 1 (rolling) B) Wheel 2 (sliding) C) Both will get down in the same time