Four identical-looking metal disks (labeled A, B, C

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

Problem

Four identical-looking metal disks (labeled A, B, C, and D) are mounted on horizontal, nearly frictionless axles in the laboratory. Each disk is spun up by an electric motor and then allowed to spin freely. A photogate measures the instantaneous angular speed

\omega

of each disk just after the motor is disengaged. The rotational kinetic energy

K_{\text{rot}}

stored in each disk at that instant is the same and equal to

40\,\text{J}

. The measured angular speeds are shown in the table below.

Disk	Angular speed $\omega$ ( $\text{rad}\,\text{s}^{-1}$ )
A	9.0
B	12.0
C	15.0
D	18.0

(1) Part 1: (a) For disk A, calculate the rotational inertia about its axle. Express your answer with the correct units. (2) Part 2: (b) Rank the four disks from greatest to least rotational inertia. Justify your ranking without performing additional calculations. (3) Part 3: (c) Suppose disk C is a solid uniform disk of mass

2.0\,\text{kg}

and unknown radius

R

. Use your result from part (b) together with appropriate reasoning to determine

R

. Clearly indicate how you arrive at your answer.

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