Non-Equilibrium Suppose an object moves in a circle and speeds up: F t =ma t F t r=ma t r =m(αr)r= mαr 2 τ= mr 2 α

Moment of Inertia I= mr 2 :moment of inertia τ= I α (for a single object) Note the similarity to F=ma!

τ 1 = m 1 r 1 2 α τ =∑τ i = ∑ m i r i 2 α= (∑ m i r i 2 )α I= ∑ m i r i 2 ∑ τ= I α (for any solid object) Note similarity to ∑ F= ma r1r1

A light, 1.00m stick has a 3.00kg attached to one end, and a 2.00kg mass attached to the other. Find the moment of inertia relative to an axis perpendicular to the rod a) and through its midpoint b) and through its center of gravity. 1.00m 3.00kg 2.00kg

For each axis of the system on the previous slide, find the minimum amount of force that must be applied to the 3kg mass alone that will cause the stick to go from rest to 5.00s -1 in 2.00s.

HW: read bottom of ; Do 31,32