velocity decreases. In contrast, pulling the weights close in to her body decreases her
moment of inertia and increases her angular velocity.
Ice skaters apply this principle skillfully. When they wish to spin rapidly, they wrap their
arms tightly around their bodies. They decrease their moment of inertia to increase their
angular velocity. You can see images of a skater applying this principle to the right and
above.
Conservation of angular
momentum
Li = Lf
IiȦi = IfȦf
L= angular momentum
I = moment of inertia
Ȧ = angular velocity
The skater pulls in her arms,
cutting her moment of inertia in
half. How much does her angular
velocity change?
IiȦi = IfȦf
IiȦi = (½Ii)Ȧf
Ȧf = 2Ȧi (it doubles)
10.12 - Gotchas
A torque is a force. No, it is not. A net torque causes angular acceleration. It requires a force.
A torque that causes counterclockwise acceleration is a positive torque. Yes, and a torque that causes clockwise acceleration is negative.
I have a baseball bat. I shave off some weight from the handle and put it on the head of the bat.A baseball player thinks I have changed the
bat’s moment of inertia. Is he right? Yes. A baseball player swings from the handle, so you have increased the amount of mass at the farthest
distance, changing the bat’s moment. The player will find it harder to apply angular acceleration to the bat.
A skater begins to rotate more slowly, so his angular momentum must be changing. Not necessarily. An external torque is required to change
the angular momentum. The slower rotation could instead be caused by the skater altering his moment of inertia, perhaps by moving his hands
farther from his body. On the other hand, if he digs the tip of a skate into the ice, that torque would reduce his angular momentum.