Spinning Disk - Angular Speed

[cstout]

Homework Statement

A disk with a radial line painted on it is mounted on an axle perpendicular to it and running through its center. It is initially at rest, with the line at theta 0 = -90°. The disk then undergoes constant angular acceleration. After accelerating for 3.1 s, the reference line has been moved part way around the circle (in a counterclockwise direction) to theta f = 130°.

Given this information, what is the angular speed of the disk after it has traveled one complete revolution (when it returns to its original position at -90°)?

Homework Equations

w = lim(change in theda)/(change in time)

The Attempt at a Solution

change in theda is 140 degrees

change in time is 3.1 seconds

 

[G01]

This is a problem involving a constant angular acceleration and you need to use that information to solve this problem.

HINT:

Can you state the kinematic equations for rotational motion?

 

[Moetasim]

w = (140 degrees) / (3.1 seconds) = 45.16 degrees/second

The angular speed of the disk after one complete revolution would be 45.16 degrees/second. This means that the disk is rotating at a constant rate of 45.16 degrees per second, and it would take approximately 8.8 seconds for the disk to complete one full revolution. It is important to note that this calculation assumes that the disk maintains a constant angular acceleration throughout its rotation. Any changes in the acceleration could result in a different angular speed.