A disk with a radial line painted on it is mounted on an axle perpendicular to i

Question

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°)?

Explanation / Answer

The initial position at -90o is along the negativ y axis.

Since it moves counterclockwise to +130 deg that is an angular distance of 90+130 = 220 deg

use pi rad = 180 deg

so 220 deg = 3.84 rad

Then apply the formula

= ot + 0.5 t2

3.84 = (0) + (.5)()(3.12)

= .799 rad/s2

Use that acceleration to find the velocity after one complete revolution, which is 2 radians

Use f2 = o2 + 2

f2 = (0) + (2)(.799)(2)

f = 3.17 rad/s

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