A turntable initially rotates at

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

Problem

33\tfrac{1}{3}\,\text{rev\,min}^{-1}

. A mark on its rim is observed for a total time of

2.5\,\text{min}

. At the instant

t = 1.5\,\text{min}

, the rotation rate is suddenly increased (instantaneously) to

66\tfrac{2}{3}\,\text{rev\,min}^{-1}

and remains constant at this higher value for the remainder of the observation. Ignore the brief transition interval. (a) Calculate the angular displacement of the mark during the first

1.5\,\text{min}

. (b) Determine its angular displacement during the next

1.0\,\text{min}

while the turntable is rotating at the higher speed. (c) Express the total angular displacement for the entire

2.5\,\text{min}

observation as: (i) the number of complete revolutions, and (ii) the additional angle (in degrees) beyond those whole revolutions. (d) If the radius of the rim is

0.15\,\text{m}

, calculate the total distance travelled by the mark along the circular path during the

2.5\,\text{min}

. Provide detailed calculations and state your answers with correct units.

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