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A bicyclist starting at rest produces a constant angular acceleration of 1.30 rad/s² for wheels that are 39.0 cm in radius. (a) What is the bicycle's linear acceleration (in m/s²)?

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The problem describes a bicyclist starting at rest and producing a constant angular acceleration of 1.30 rad/s² for wheels, where the radius is given as 39.0 cm. We are asked to find the bicycle's linear acceleration (in m/s²).

Linear acceleration is related to angular acceleration by the formula:

a = r * alpha

Where:
- a is the linear acceleration,
- r is the radius of the wheel, and
- alpha is the angular acceleration.

First, we need to convert the radius of the wheels from cm to m by dividing by 100. This gives us:

r = 39 cm ÷ 100 = 0.39 m

The angular acceleration is already given in the appropriate unit , rad/s², so we have:

alpha = 1.30 rad/s²

Next, we substitute these values into our formula:

a = r * alpha
a = 0.39 m * 1.30 rad/s²

Calculating these numbers, the linear acceleration equals 0.507 m/s².

Therefore, the bicycle's linear acceleration is 0.507 m/s².

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