Question

Please answer all parts. Thank you!

1. Explain the correspondence that lets us easily translate between linear motion and rotational motion. What are the linear analogues of the rotational quantities we have discussed in lecture i.e. angle, angular velocity, angular acceleration and moment of inertia? Where does the correspondence seem to fail?

2. Explain, in words, how we know that a freely spinning asteroid in space is rotating about an axis that passes through its center of mass?

3. You are handed a rod that is three times as dense on one end as it is on the other end. Find the moment of inertia when the axis of rotation is about the heavy end, and find the moment of inertia when the axis of rotation is about the light end.

4. Suppose we have two blocks of masses m1 and m2. The block with mass m1 is moving towards block m2 at speed v. After the collision, we measure the total kinetic energy and find that the total kinetic energy after the collision is m2/(m1+m2) less than the kinetic energy before the collision. Find the final speeds of the two blocks. What type of collision is this?

5. A merry-go-round starts at rest, and begins accelerating clockwise at 0.1 radians per second per second.

a. How long will it take to reach its maximum angular velocity of 5 revolutions per minute?

b. How many times will the merry-go-round have completed a revolution before it reaches its maximum angular velocity? If it's not a whole number of revolutions, include the amount of partial revolutions.

Answer 1