Question

A torque of 0.77 N⋅m is applied to a bicycle wheel of radius 45 cm and mass 0.90 kg. Calculate the angular acceleration of the wheel.

Answer 1

To find the angular acceleration of the bicycle wheel, use the formula angular acceleration = torque / moment of inertia. In this case, the moment of inertia of the wheel is (1/2) * mass * radius^2. By substituting the given values, we find that the angular acceleration is approximately 0.38 rad/s^2.

Step-by-step explanation:

To calculate the angular acceleration of the bicycle wheel, you can use the formula:

angular acceleration = torque / moment of inertia

The moment of inertia of a solid disk, such as a bicycle wheel, is given by:

moment of inertia = (1/2) * mass * radius^2

By substituting the given values, we have:

moment of inertia = (1/2) * 0.9 kg * (0.45 m)^2

Next, we can calculate the angular acceleration:

angular acceleration = 0.77 N⋅m / ((1/2) * 0.9 kg * (0.45 m)^2)

Plugging in the values, we get:

angular acceleration ≈ 0.38 rad/s^2