work in rotation

Work in Rotation

§ 10.3–10.4

Rolling without slipping

Circular body of radius R

vcm = R

R

vcm

Energy of Rolling Bodies

• Krot (edge axis)

• Ktrans + Krot (center of mass) axis

R

vcm

Rotational Work

dW = F·dsds

F

R

ddW = ·d

Power

• The rate of doing work

• dW/dt• ·d/dt = ·

Poll Question

You apply equal torques to two different cylinders initially at rest, one of which has a moment of inertia twice as large as the other. After one complete rotation, which cylinder rotated the farthest?

A. The cylinder with the larger I.B. The cylinder with the smaller I.C. Both rotated through the same

angle.

I 2I

Poll Question

You apply equal torques to two different cylinders initially at rest, one of which has a moment of inertia twice as large as the other. After one complete rotation, on which cylinder was the most work done?

A. The cylinder with the larger I.B. The cylinder with the smaller I.C. Both had the same amount of

work done.

I 2I

Poll Question

You apply equal torques to two different cylinders initially at rest, one of which has a moment of inertia twice as large as the other. After one complete rotation, which cylinder has the greatest kinetic energy?

A. The cylinder with the larger I.B. The cylinder with the smaller I.C. Both have the same K.

I 2I

Poll Question

You apply equal torques to two different cylinders initially at rest, one of which has a moment of inertia twice as large as the other. After one complete rotation, which cylinder has the greatest angular speed?

A. The cylinder with the larger I.B. The cylinder with the smaller I.C. Both have the same .

I 2I

Poll Question

You apply equal torques to two different cylinders initially at rest, one of which has a moment of inertia twice as large as the other. Which completed the rotation in the shortest time?

A. The cylinder with the larger I.B. The cylinder with the smaller I.C. Both took the same time.

I 2I

Poll Question

You apply equal torques to two different cylinders initially at rest, one of which has a moment of inertia twice as large as the other. To which cylinder was the greatest power applied?

A. The cylinder with the larger I.B. The cylinder with the smaller I.C. Both received the same power.

I 2I

Example Problem

A solid ball is released from rest and rolls down a slope with angle 65° below horizontal.

a) What minimum coefficient of static friction must be between the ball and the slope for no slipping?

b) What is the total kinetic energy after 2 s if m = 1 kg and r = 2 m?

r