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 q0 = -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 qf = 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°)?
|w| = rad/s
It is not certain to me what the measurement of angles is, and the impact of counterclockwise. It matters.
I assume the displacement was 90+130=220deg . Assuming the other direction would have been 140 deg.
Assuming 220 deg, then
220deg/360deg * 2PI=1/2 angacc*time
solve for angacceleration.
then:
wf^2=2*angacceleration*2PI
watch your units
To find the angular speed of the disk after one complete revolution, we need to determine the change in angle and the time it took for the disk to complete one revolution.
The change in angle can be calculated by subtracting the initial angle from the final angle:
Δq = qf - q0
Δq = 130° - (-90°)
Δq = 220°
Since one complete revolution is equal to 360°, the disk has traveled 220° in less than one revolution.
The time it took for the disk to reach the final angle can be determined from the given information. The disk underwent constant angular acceleration for 3.1 seconds.
Now, to find the angular speed, we need to divide the change in angle by the time it took:
Angular speed = Δq / t
Angular speed = 220° / 3.1 s
However, the angular speed is typically measured in radians per second rather than degrees. So, we need to convert the angle from degrees to radians:
1 radian = 180°/π
Angular speed = (220° / 3.1 s) * (π / 180°)
Calculating this expression will give you the angular speed in radians per second (rad/s).