**Chapter
10; Rotational Kinematics and Energy **

**| ToC,
Chapter 10 | Course Calendar
|**

**D10.1** It requires 6 seconds for a phonograph
turntable initially rotating at 33 rpm to reach 45 rpm. Assume the angular acceleration
is uniform. How many revolutions are made during this time?

**D10.2** A ventilator fan is turning at
600 rpm when the power is cut off and it turns through 1000 revolutions while
coasting to a stop. Find the angular acceleration and the time required to stop.

**D10.3** A solid, uniform
cylinder of 12 cm radius with mass of 5.0 kg is free to rotate about its symmetry
axis. A cord is wound around the drum and a 1.2 kg mass is attached to the
end of the cord. Find the acceleration of the hanging mass, the angular acceleration
of the cylinder, and the tension in the cord.

**D10.4** A 10 kg block sits on a horizontal
surface with coefficient of friction of 0.2 between the block and the surface.
A string runs from this block over a wheel of radius 10 cm and moment of inertia
of 2.0 kg m^{2} and is attached to a hanging 5 kg mass. Find the acceleration
of the masses, the angular acceleration of the wheel, and the tension in the
string on each side.

**D10.5** Assume a playground merry-go-round
to be a uniform cylinder or disk of 150 kg and 1.8 m radius. What is its moment
of inertia?

It is initially at rest when a 50 kg child, running at 4 m/s, in a direction tangential to the edge of the merry-go- round, jumps on. What is its angular velocity after the child sits down on the edge?

**D10.6** What is the kinetic energy of
tire with moment of inertia of 60 kg m^{2} that rotates at 150 rpm?

**D10.7** A disk rolls without slipping
down a hill of height 10.0 m. If the disk starts from rest at the top of the
hill, what is its speed at the bottom?

**D10.8** An Atwood's machine is composed
of a 2-kg mass and a 2.5-kg mass attahed to a string hanging over a wheel that
has a radius of 10 cm and a moment of inertia of 12.5 kg-m^{2}. The
2.5-kg mass is initially 1.0 m above the floor. Use conservation of energy to
find the speed of this mass just before it hits the floor.

**D10.9** A basket of tomatoes of mass 20.0
kg is being hoisted by a windlass. The rope is wrapped around an axle that is
a solid cylinder of wood having a radius of 0.1 m and a mass of 10 kg. The mass
of the crank handles is neglibible. The operator lets go of the handle when
the basket is 6 m above the ground. With what linear speed does the basket strike
the ground?

**D10.10** To demonstrate conservation of
angular momentum a Physics professor stands on a frictionless turntable with
a 2 kg mass in each outstretched hand. An assistant gives her a small initial
angular velocity of 2 rad/s. She then drops her hands to her sides and her angular
velocity increases dramatically. As a rough estimate, consider her arms to have
mass of 5 kg each and to be 1 m long rods hinged at the axis of rotation. The
rest of her body has an approximate moment of inertia of 0.55 kg m^{2}.
Find her final angular velocity when the masses are 0.25 m from the axis of
rotation. Calculate the initial and final values of the rotational kinetic energy
and explain the cause of the difference in these values.**
**

(c) 2005, Doug Davis; all rights reserved** .**