A torque of 12 N ? m is applied to a solid, uniform disk of radius 0.50 m. If the disk accelerates at $1.6 \mathrm { rad } / \mathrm { s } ^ { 2 }$ what is the mass of the disk?
A) 60 kg
B) 45 kg
C) 30 kg
D) 15 kg

Question

Quizplus · Accepted Answer

The torque applied to the disk is given by:$$\tau = I \alpha$$where $I$ is the moment of inertia of the disk and $\alpha$ is the angular acceleration. The moment of inertia of a solid, uniform disk is given by:$$I = \frac{1}{2}MR^2$$where $M$ is the mass of the disk and $R$ is the radius of the disk. Substituting these expressions into the torque equation, we get:$$\tau = \frac{1}{2}MR^2 \alpha$$Solving for $M$, we get:$$M = \frac{2\tau}{R^2 \alpha}$$Substituting the given values, we get:$$M = \frac{2(12 \mathrm { N } \cdot \mathrm { m })}{(0.50 \mathrm { m })^2 (1.6 \mathrm { rad } / \mathrm { s } ^ { 2 })}$$$$M = 60 \mathrm { kg }$$Therefore, the mass of the disk is 60 kg.

A Torque of 12 N ? M Is Applied to a Solid