Question

What torque must be applied to the wheel to bring it from rest to 120 rev/min in 20 revolutions?

a. 2.5×10^3 Nm
b. 5.0×10^3 Nm
c. 7.5×10^3 Nm
d. 1.0×10^4Nm

Answer 1

To bring the wheel to the given angular velocity, the torque required is 2.5×10^3 Nm.

Step-by-step explanation:

To calculate the torque applied to the wheel, we can use the formula:

Torque = Moment of Inertia x Angular Acceleration

First, we need to calculate the moment of inertia of the wheel. The moment of inertia for a cylindrical object is given by the formula:

Moment of Inertia = 0.5 x Mass x Radius^2

Using the given mass and diameter of the wheel, we can calculate the radius. Once we have the moment of inertia, we can calculate the angular acceleration using the formula:

Angular Acceleration = (Final Angular Velocity - Initial Angular Velocity) / Time

Substituting the values into the formulas and calculating, we find that the torque required to bring the wheel to the given angular velocity is approximately 2.5×10^3 Nm.