A uniform solid disk with a mass of 40.3 kg and a radius of 0.454 m is free to rotate about a frictionless axle. Forces of 90.0 N and 125 N are applied to the disk
(a) What is the net torque produced by the two forces? (Assume counterclockwise is the positive direction
(b) What is the angular acceleration of the disk?
This is how i solved it.
Torque = Fl
net torque = (125N x 0.454m) + (90N x 0.454N)=97.81
Angular acceleration = torque/ inertia
Inertia = mass x radius ^2
= 40.3 kg x 0.454 ^2 =8.31
Angular acceleration = 97.81/ 8.31 =11.77 rads/s^2
Please check solution
Isnt the moment of inertia 1/2 m r^2 ?
So Moment of Inertia = 0.5x 40.3kg x 0.454^2 = 4.15
Angular acceleration =97.81/4.15
=23.55
rads/s^2
You are correct, the moment of inertia for a solid disk rotating about its axis is given by the formula 1/2 * mass * radius^2.
So, the correct moment of inertia for the given disk is:
Moment of inertia = 0.5 * 40.3 kg * (0.454 m)^2 = 4.15 kg*m^2
Using this moment of inertia, we can calculate the angular acceleration:
Angular acceleration = net torque / moment of inertia
Substituting the values, we have:
Angular acceleration = 97.81 N*m / 4.15 kg*m^2 ≈ 23.6 rad/s^2
Therefore, the correct angular acceleration is approximately 23.6 rad/s^2.
You are correct that the moment of inertia for a solid disk rotating about its axis is 1/2 * mass * radius^2. Let's recalculate the solution using the correct moment of inertia.
(a) To find the net torque produced by the two forces, you correctly used the formula Torque = Force * lever arm. The lever arm is the radius of the disk, which is 0.454 m. The torques produced by the two forces can be added together because they are acting in the same direction (counterclockwise in this case).
Net torque = (125 N * 0.454 m) + (90 N * 0.454 m) = 97.81 N·m
(b) To find the angular acceleration of the disk, you can use the formula Angular acceleration = Torque / Moment of inertia. As you mentioned, the correct moment of inertia for a solid disk is 0.5 * mass * radius^2.
Moment of inertia = 0.5 * mass * radius^2 = 0.5 * 40.3 kg * (0.454 m)^2 = 4.15 kg·m^2
Angular acceleration = 97.81 N·m / 4.15 kg·m^2 = 23.55 rad/s^2
So, the correct angular acceleration of the disk is indeed 23.55 rad/s^2.