Homework Help: Rotation

Page 108
5. (a) Find change in angular velocity. (b) Use angular constant acceleration equations on page 103.
7. The force asked for is the force that creates the torque that changes the speed. Find the angular acceleration, then use 2nd law for rotation to find torque. Assume the merry-go-round is a disk for the rotational inertia. The applied force must be enough to create the torque plus overcome the frictional force. (325 N)

Page 124
7. Rotary work problem: calculate torque, multiply times angular displacement. Watch the units!
11. Rotary work must equal linear work in this case. Weight times height equals torque times angular displacement. Convert to revolutions.

Page 130
5. Assume the wheel is a thin ring. Refer to p. 105 for rotational inertia. Be sure all quantities are in fundamental units.
9. (a) Assume the earth is a solid sphere. Get the mass and radius from p. 66. Assume 1 day = 24 hours. Calculate angular speed in fundamental units. (b) Use 1.50 x 10¹¹ m as the radius of the earth's orbit.
10. (a) Ball has both rotary and linear kinetic energy. To find the rotary energy, use the rotational inertia for a solid sphere found on page 105. Express angular velocity in terms of linear velocity and radius. When rotational inertia and angular velocity spuared are multiplied together, the radius cancels out and is therefore not necessary for the problem. (b) Ball will roll up the incline until all kinetic energy is converted to potential energy. Set these quantities equal and solve for h. Remember, this is the vertical height, not the distance up the plane. Use trig to find the distance.