A large grinding wheel in the shape of a solid cylinder of radius 0.330 m is free to rotate on a frictionless, vertical axle. A constant tangential force of 210 N applied to its edge causes the wheel to have an angular acceleration of 1.161 rad/s2.
(a) What is the moment of inertia of the wheel?
To find the moment of inertia of the wheel, we can use the formula:
Moment of Inertia (I) = (Torque (τ)) / (Angular Acceleration (α))
In this case, the torque can be calculated using the formula:
Torque (τ) = Force (F) * Radius (r)
First, let's calculate the torque:
τ = F * r
= 210 N * 0.330 m
= 69.3 N·m
Next, we can substitute the torque and angular acceleration into the moment of inertia formula:
I = τ / α
= 69.3 N·m / 1.161 rad/s^2
≈ 59.74 kg·m^2
Therefore, the moment of inertia of the wheel is approximately 59.74 kg·m^2.