Question

An old grindstone, used for sharpening tools, is a solid cylindrical wheel that can rotate about its central axle with negligible friction. The radius of the wheel is 0.330 m. A constant tangential force of 200 N applied to its edge causes the wheel to have an angular acceleration of 0.804 rad/s2.

(a) What is the moment of inertia of the wheel (in kg · m2)?

_________kg · m2

(b) What is the mass (in kg) of the wheel?

__________kg

(c) The wheel starts from rest and the tangential force remains constant over a time period of 4.50 s. What is the angular speed (in rad/s) of the wheel at the end of this time period?

__________rad/s

Answer 1

(a)

The torque on the wheel due to the tangential force is

where R=0.330 meters is the radius of the wheel and F=200 N is the tangential force on the wheel.

By Newton's second law of motion, the angular acceleration of the wheel is given by

where I is the moment of inertia of the wheel.

Substituting values

(b)

The moment of inertia of a cylinder of radius R and mass M is given by

Solving for mass

Substituting values

(c)

The wheel starts from rest, initial angular speed of the wheel is

The angular acceleration is constant, the angular motion is governed by the kinematics equations for uniformly accelerated motion. To find the angular velocity after time t=4.50 seconds we use

Substituting values