Help needed for physics written questions

1. Explain the difference between linear speed and rotational speed. Include formula difference and how rotational speed is changed to linear speed.

2. A bicycle has wheels with a 30-centimeter radius. If smaller wheels with a 25-centimeter radius are installed, what is the change in linear speed of the bicycle if the wheels rotate at 1 revolution per second?

3. In terms of rotational inertia, explain why:

a. It’s hard to walk without bending your knees.

b. Short-legged people step more quickly than long-legged people do.

c. You can swing a baseball bat faster than a long one of the same weight.

4.Answer the following questions:

a.              Explain how skaters can quickly go from a slow to fast spin and vice versa.

b.              What happens to their angular velocity and moment of inertia?

c.              Is an external torque required? Explain.

5.              What is a gyroscope and how is it used as a navigational aid?

6.              To tighten a bolt, you push with a force of 80 Newtons at the end of a wrench handle that is 0.25 meters from the axis of the bolt.

a.              What torque are you exerting?

b.              If you move your hand inward to be only 0.10 meters from the bolt, what force do you have to exert to achieve the same torque?

c.              Do your answers depend on the direction of your push relative to the direction of the wrench handle?