A solid disk with a mass of 100kg and a radius of 0.2m, turns clockwise through an angular displacement 10 rad when starting from rest to attain its maximum angular speed, of 1 revolution every 0.5s. What is the angular acceleration that the wheel experienced in order to attain maximum speed? How much time did it take for the disk to go from rest to maximum angular speed?
1 rev/0.5s = 2 rev/s
-> 12.57 radians/s
= final angular velocity = wf
Time required = 10 rad / (average angular velocity wf/2
= 10/6.28 = 1.59 s
Angular acceleration = wf/t
= 7.9 rad/s^2
The mass and radius of the wheel are not needed to answer the questions, but would be needed for the required torque.
To calculate the angular acceleration, we can use the following equation:
angular acceleration (α) = (change in angular velocity) / (change in time)
We know that the disk goes from rest to a maximum angular speed of 1 revolution every 0.5 seconds.
Now, we need to convert this angular speed into radians per second. Since there are 2π radians in one revolution, the angular speed is:
Angular speed = 1 revolution / 0.5 seconds = (1 revolution / 0.5 seconds) x (2π radians / 1 revolution) = 4π radians per second
So, the change in angular velocity is 4π radians per second.
Now, let's calculate the change in time. We know that the disk starts from rest and reaches maximum speed, so the change in time is simply the time it takes to go from rest to maximum speed, which is 0.5 seconds.
Therefore, the angular acceleration is:
Angular acceleration (α) = (change in angular velocity) / (change in time) = (4π radians per second) / (0.5 seconds) = 8π radians per second squared.
So, the angular acceleration that the wheel experienced to attain maximum speed is 8π radians per second squared.
The time it took for the disk to go from rest to maximum angular speed is 0.5 seconds.