A uniform disk with a mass of 27.3 kg and a radius of 0.309 m is free to rotate about a frictionless axle. Forces of 90.0 N and 125 N are applied to the disk, as the drawing indicates.
(a) What is the net torque produced by the two forces?
(b) What is the angular acceleration of the disk?
The drawing is needed to show where and in what directions the forces are applied to the disk.
Compute net torque.
angular acceleration =
(Net Torque)/(Moment of inertia)
To find the answers to these questions, we need to apply the principles of rotational mechanics. The net torque produced by the forces can be found using the equation:
Net Torque = Force × Lever Arm
The lever arm is the perpendicular distance from the axis of rotation to the line of action of the force. In this case, since the forces are applied tangentially to the disk, the lever arm is equal to the radius of the disk.
(a) Net torque produced by the two forces:
The torque produced by the 90.0 N force is given by:
Torque1 = Force1 × Lever Arm = 90.0 N × 0.309 m
The torque produced by the 125 N force is given by:
Torque2 = Force2 × Lever Arm = 125 N × 0.309 m
To find the net torque, we need to add these two torques together:
Net Torque = Torque1 + Torque2
(b) Angular acceleration of the disk:
To find the angular acceleration of the disk, we can use the equation:
Net Torque = Moment of Inertia × Angular Acceleration
The moment of inertia, I, for a uniform disk rotating about its axis is given by:
I = (1/2) × mass × radius^2
Substituting the given values for mass and radius, we can find the moment of inertia. Then, rearranging the equation, we can solve for angular acceleration:
Angular Acceleration = Net Torque / Moment of Inertia
Now, let's calculate the answers using the given values and the equations above.