1. A student sits on a freely rotating stool holding two weights, each of mass 3.09 kg. When his arms
are extended horizontally, the weights are 0.94 m from the axis of rotation and he rotates with an
angular speed of 0.755 rad/s. The moment of inertia of the student plus stool is 3.09 kg∙m2 and is
assumed to be constant. The student pulls the weights inward horizontally to a position 0.307 m
from the rotation axis.
(a) Find the new angular speed of the student. (rad/s)
(b) Find the kinetic energy of the rotating system before and after he pulls the weights inward. (Joule)
2. A 54.0 kg woman stands at the rim of a horizontal turntable having a moment of inertia
of 495 kg∙m2 and a radius of 2.00 m. The turntable is initially at rest and is free to rotate about a
frictionless, vertical axle through its center. The woman then starts walking around the rim
clockwise (as viewed from above the system) at a constant speed of 1.50 m/s relative to the Earth.
(a) In what direction and with what angular speed does the turntable rotate?
3. A projectile of mass m moves to the right with a speed vi (Fig. P11.50a). The projectile strikes and
sticks to the end of a stationary rod of mass M, of length d, that is pivoted about a frictionless axle
through its center (Fig. P11.50b). (Use any variable or symbol stated above as necessary.)
a)
Find the angular speed of the system right after the collision.
b) Determine the fractional loss in mechanical energy due to the collision.