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A point on the edge of a disk rotates around the center of a disk with and initial angular velocity of 3rad/s clockwise. The graph shows the point’s angular acceleration as a function of time. The positive direction is considered to be counterclockwise. All frictional forces are considered to be negligible. Which of the following graphs qualitatively represents the angular velocity w of the point on the disk as a function of time t between 0 s to 2 s?

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MathPhys

Answer:

D

Explanation:

The graph shows a constant angular acceleration of 6 rad/s².

For constant acceleration, the angular velocity is:

ω = ω₀ + αt

where ω₀ is the initial angular velocity, α is the angular acceleration, and t is time.

In this case, ω₀ = -3 rad/s (since clockwise is negative). Therefore, the equation for the angular velocity is:

ω = -3 + 6t

This is a line with a positive slope and negative y-intercept, so the answer is D.

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