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.