A solid uniform disk of radius and mass is rigidly attached to a motor shaft

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

Problem

A solid uniform disk of radius

0.15\,\text{m}

and mass

2.0\,\text{kg}

is rigidly attached to a motor shaft. The shaft is held in place so that the center of the disk remains fixed in space while the disk spins about its central axis. The motor brings the disk from rest to an angular speed of

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

2.0\,\text{s}

under constant angular acceleration. (a) Determine the magnitude of the disk’s kinetic energy when it reaches

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

. (b) Calculate the average power delivered by the motor to the disk during the

2.0\,\text{s}

spin-up interval. (c) If the motor is switched off and friction at the axle brings the disk uniformly to rest in

6.0\,\text{s}

, find the magnitude of the frictional torque acting on the disk. (d) Explain why the translational kinetic energy of the disk is zero throughout the entire motion, yet mechanical power is still required to spin it up.

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