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Q. 42

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Physics for Scientists and Engineers: A Strategic Approach with Modern Physics
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Short Answer

A bicycle wheel is rotating at , and when the cyclist begins to pedal harder, giving the wheel a constant angular acceleration of .

a. What is the wheel's angular velocity, in rpm, later?

b. How many revolutions does the wheel make during this time?

Part (a) The angular velocity of the wheel after is .

Part (b) The number of revolutions made by the wheel in is

See the step by step solution

Step by Step Solution

Part (a) Step 1. Given information

The bicycle wheel is rotating at , and when the cyclist begins to pedal harder it gives the wheel a constant angular acceleration of .

Part (a). Step 2. Explanation

The angular velocity of the wheel after is,

, is the angular velocity of the wheel after , is the initial angular velocity of the wheel, is the angular acceleration of the wheel, is the period of time.

Substitute for for and for in the above equation to find .

Thus, the angular velocity of the wheel after is .

Part (b) Step 1. Given information

Given info: The bicycle wheel is rotating at , and when the cyclist begins to pedal harder it gives the wheel a constant angular acceleration of .

Part (b).  Step 2. Explanation

The revolution made by the wheel in is,

Here, is the angular displacement in , and is the number of revolution made by the wheel in .

The angular displacement made by the wheel in is,

Here, is the initial angular velocity of the wheel, is the angular acceleration of the wheel, and is the period of time.

Thus, the angular displacement of the wheel in is .

Substitute for in the equation (I) to find .

Therefore, the number of revolution made by the wheel in is .

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