A torque of 12 N ∙ m is exerted on 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 on a solid, uniform disk is given by:$$\tau = I \alpha$$where:* $\tau$ is the torque (in N m)* $I$ is the moment of inertia (in kg m^2)* $\alpha$ is the angular acceleration (in rad/s^2)The moment of inertia of a solid, uniform disk is given by:$$I = \frac{1}{2}MR^2$$where:* $M$ is the mass (in kg)* $R$ is the radius (in m)Substituting the given values into the first equation, we get:$$12 \text{ N m} = \frac{1}{2}M(0.50 \text{ m})^2(1.6 \text{ rad/s}^2)$$Solving for $M$, we get:$$M = \frac{2(12 \text{ N m})}{(0.50 \text{ m})^2(1.6 \text{ rad/s}^2)} = 60 \text{ kg}$$Therefore, the mass of the disk is 60 kg.

A Torque of 12 N ∙ M Is Exerted on a Solid,uniform