A student places a rigid

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Torque and Rotational Dynamics · Torque and Rotational Dynamics

Problem

A student places a rigid, uniform hoop on a nearly frictionless turntable. The hoop is initially at rest. The student briefly taps the rim to set it spinning and then allows it to rotate freely. A motion-sensor records the angular velocity

\omega

of the hoop every

0.20\,\text{s}

for a total of

6.0\,\text{s}

. The collected data are described below: • From

t=0

t=1.0\,\text{s}

\omega

rises linearly from

0

6.0\,\text{rad}\,\text{s}^{-1}

. • From

t=1.0\,\text{s}

t=6.0\,\text{s}

\omega

remains constant at

6.0\,\text{rad}\,\text{s}^{-1}

within the sensor’s resolution of

\pm0.1\,\text{rad}\,\text{s}^{-1}

. The student claims that the hoop is in rotational equilibrium during the

1.0\,\text{s}

–

6.0\,\text{s}

interval. (a) Describe the condition that must be satisfied for a system to be in rotational equilibrium. (b) Using the verbal description of the

\omega

–time data, explain whether the hoop meets this condition during the time interval

1.0\,\text{s}\le t\le6.0\,\text{s}

. Your explanation must explicitly connect the observed angular motion to the required torque condition. (c) Explain why the hoop cannot be in rotational equilibrium during

0\le t<1.0\,\text{s}

, even though the same turntable is used. (d) Identify one real-world factor that could prevent perfect rotational equilibrium during

1.0\,\text{s}\le t\le6.0\,\text{s}

and discuss qualitatively how this factor would appear in an ideal

\omega

–time graph.

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