Question

A rotating wheel with diameter 0.640 mm is speeding up with constant angular acceleration. The speed of a point on the rim of the wheel increases from 3.00 m/s to 6.00 m/s while the wheel turns through 4.00 revolutions. What is the angular acceleration of the wheel?

Answer 1

The angular acceleration of the wheel is 0.119 m/s².

Step-by-step explanation:

The angular acceleration of a rotating wheel can be calculated using the formula:

angular acceleration = (change in angular velocity) / (change in time)

In this case, the change in angular velocity is the difference between the final and initial velocities, which is 6.00 m/s - 3.00 m/s = 3.00 m/s. The change in time is the time it takes for the wheel to turn through 4.00 revolutions. Since each revolution is equivalent to 2π radians, the wheel turns through 4.00 revolutions * 2π radians/revolution = 8π radians.

Substituting these values into the formula, we have:

angular acceleration = (3.00 m/s) / (8π radians) = 0.119 m/s²