spinning, spinning

Please show your work on the back of this page, or on an attached page.

1) A spinning thing spins at 3.50 rad/sec. If it were accelerating at 0.55 rad/sec², what angular distance must be moved until it is spinning at 5.75 rad/sec?

2) Another spinning thing spins at 2.15 rad/sec when it begins accelerating at 1.50 rad/sec². How much time must elapse before it is moving at 8.50 rad/sec?

3) Yet another spinning thing accelerates at 0.25 rad/s². It continues accelerating at this rate until it has swept a 1.90 rad angle. The movement took 1.75 sec. What was its original angular speed?

4) An astronaut-in-training is placed inside a large centrifuge and spun rapidly to find whether she can hold her space lunch. If the radius of the centrifuge is 15 m, at what constant tangential velocity must she be spun to be subject to a centripetal acceleration 9 times that of free fall?

5) A 3.0 kg rock is twirled in a horizontal circular orbit at the end of a string of length 2.5 m. The rock makes three revolutions in five seconds. What is the tension in the string?

6) First, write the rotational equivalent for Newton’s 2^nd Law. A tangential force of 75 N is applied to the edge of a 3.0 kg disc initially at rest. The radius of the disc is 0.35 m, and the equation for its moment of inertia is (1/2)mr². Find a then calculate w after the disc has spun two rotations.

7) A man is standing, for some reason, on a spinning turntable with a weight in each hand. His moment of inertia with arms outstretched is 16 kgm². With his arms by his side his moment of inertia is 6.4 kgm². With arms outstretched he makes one rotation in two seconds. What is his angular velocity with his arms at his sides? Give your answer in radians/sec.

8) Impulse equals the change in momentum. Set up the equivalent equation for rotation, then solve this one. A 4.5 kg sphere with a 0.25 m radius is spinning at 7.5 rad/sec. How much torque is needed to bring it to a stop in 1.5 seconds? How much force, applied perpendicular to the radius, is needed to bring it to a stop in 1.5 seconds? The equation for the moment of inertia of a solid sphere is (2/5)mr².

9) A ball is rolling along at an angular speed of 0.50 rad/sec. What is its angular kinetic energy? The ball’s radius is 0.80 m, its mass is 1.2 kg and its moment of inertia equals (2/5)mr².