Rotational Kinematics (AP1)

An object rotates with an angular speed that varies with time, as shown in the graph. How can the graph be used to determine the magnitude of the angular acceleration α of the object? Justify your selection.

• Subtract the greatest value of the angular speed from the smallest value of the angular speed, because α=Δω.

• Determine the slope of the line from 0s to 2s, because the slope represents Δω/Δt.

• Determine the area bounded by the line and the horizontal axis from 0s to 2s, because α = 1/2ωΔt.

• The angular acceleration cannot be determined without knowing the rotational inertia of the object.

Which Which of the following graphs, if any, shows the angular velocity ω of the pulley as a function of time t after the block is released from rest?

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• 10 rad/sec

• 25 rad/sec

• 50 rad/sec

• 2 rad/sec

The graph shows the angular velocity ωω as a function of time tt for a point on a rotating disk. The magnitude of the angular acceleration of the disk at t=2s is most nearly...

The graph shows the angular velocity ω as a function of time t for a point on a rotating disk. How far does the disk rotate from 0 to 4 sec?

• 32 rad

• 20 rad

• 8 rad

• 1.5 rad

A graph of the angular velocity ω as a function of time t is shown for an object that rotates about an axis. Three time intervals, 1–3, are shown. Which of the following correctly compares the angular displacement Δθ of the object during each time interval?

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