A rigid turntable rotates about a central vertical axis

PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion

Problem

A rigid turntable rotates about a central vertical axis. The graph of its angular position

\theta

(in radians) versus time

t

(in seconds) is described verbally as follows: • From

t = 0\,\text{s}

t = 5\,\text{s}

\theta

increases uniformly from

0\,\text{rad}

+10\,\text{rad}

. • From

t = 5\,\text{s}

t = 8\,\text{s}

\theta

remains constant at

+10\,\text{rad}

. • From

t = 8\,\text{s}

t = 12\,\text{s}

\theta

decreases uniformly from

+10\,\text{rad}

+4\,\text{rad}

. Take the counter-clockwise (CCW) direction to be positive. (a) Describe qualitatively how the angular velocity

\omega

behaves during each of the three time intervals stated above. In your description include the sign of

\omega

and whether its magnitude is constant, zero, or changing. (b) On appropriately labeled axes with time on the horizontal and

\omega

on the vertical, sketch a possible

\omega

–versus–time graph that is consistent with the verbal description of

\theta(t)

. Clearly label the numerical values of

\omega

at the beginning and end of each interval. (c) Identify the time interval(s), if any, during which the turntable rotates clockwise (CW). Explain how you arrived at your answer.

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