A torque of 77.7 Nm causes a wheel to start from rest , completes 5.55 revolutions and attains a final angular velocity of 88.8 rad/sec. What is the moment of inertia of the wheel? The distance is 5.55 revolutions. From this you can get the angular acceleration is revolutions. Then convert it to radians and plug it into the equation T=IW to find the moment of Inertia.
First, we need to convert the distance traveled by the wheel in revolutions to radians. Since 1 revolution is equal to 2π radians, 5.55 revolutions is equal to:
5.55 revolutions * 2π radians/revolution = 11.1π radians
Next, we can calculate the angular acceleration of the wheel using the final angular velocity and the initial angular velocity (0 rad/sec) with the formula:
angular acceleration = (final angular velocity - initial angular velocity) / time
We know that the time it took for the wheel to complete 5.55 revolutions is not given, but we can use the fact that the final angular velocity is reached at the end of the 5.55 revolutions to calculate the time taken as follows:
Time taken = distance traveled / linear velocity = 5.55 revolutions / 1 radian per revolution = 5.55 seconds
Therefore, angular acceleration = (88.8 rad/sec - 0 rad/sec) / 5.55 sec = 16 rad/sec^2
Now, we can calculate the moment of inertia of the wheel using the formula T = Iα, where T is the torque (77.7 Nm) and α is the angular acceleration (16 rad/sec^2):
I = T / α = 77.7 Nm / 16 rad/sec^2 = 4.85625 kg.m^2
Therefore, the moment of inertia of the wheel is 4.85625 kg.m^2.