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Physics: Linear vs Rotational Speed, Bicycle Speed, and Rotation

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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 you knees.
b. Short-legged people step more quickly than lopng-legged people do.
c. You can swing a basesball bat faster than a long one of the same weight.

4. 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 torgue 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 acheive the same torque?
c. Do your answers depend on the direction of your push relative to the direction of the wrench handle?

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

Solution:
Linear speed is the measure of linear distance covered by an object in a unit of time. It is measured in meter per seconds or kilometers per hour. While rotational speed is measured in revolutions per second or radians per seconds. It is result of application of torque.
Linear speed = radius*rotational 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?

Solution:
1 revolution per second = 2 radians per second
Linear speed when radius is 30 cm. = 30*2 = 30*2*3.14 = 188.4
Linear speed when radius is 25 cm. = 25*2 = 25*2*3.14 ...

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