The combination of an applied force produces a constant total torque of 39.6 N.m on a wheel rotating about a fixed axis. The applied force acts for 5.3 s. During this time, the angular speed of the wheel increases from 0 to 9.8 rad/s. Determine the moment of inertia of the wheel.
25.4
To determine the moment of inertia of the wheel, we need to use the formula for torque and angular acceleration and then rearrange the equation to solve for moment of inertia.
The formula for torque is given by:
Torque (τ) = Moment of Inertia (I) × Angular Acceleration (α)
In this case, the total torque (τ) and the angular acceleration (α) are known.
Total torque (τ) = 39.6 N.m
Angular acceleration (α) = (Final angular speed - Initial angular speed) / Time = (9.8 rad/s - 0 rad/s) / 5.3 s
Let's calculate the value of angular acceleration:
Angular acceleration (α) = 9.8 rad/s / 5.3 s = 1.849 rad/s²
Now, substitute the values into the torque formula:
39.6 N.m = I × 1.849 rad/s²
Next, rearrange the equation to solve for moment of inertia (I):
I = 39.6 N.m / 1.849 rad/s²
I ≈ 21.40 kg.m²
Therefore, the moment of inertia of the wheel is approximately 21.40 kg.m².