A torque of 12 N ∙ m is applied to a solid,uniform disk of radius 0.50 m.If the disk accelerates at 5.7 rad/s²,what is the mass of the disk?

Question

Quizplus · Accepted Answer

The torque applied to the disk is given by:$$	au = I \alpha$$where:* $	au$ is the torque (in N ∙ m)* $I$ is the moment of inertia (in kg ∙ m²)* $\alpha$ is the angular acceleration (in rad/s²)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 (in kg)* $R$ is the radius of the disk (in m)Substituting the given values into the equations above, we get:$$12 	ext{ N} \cdot 	ext{m} = \frac{1}{2}M(0.50 	ext{ m})^2$$$$12 	ext{ N} \cdot 	ext{m} = 0.125M$$$$M = \frac{12 	ext{ N} \cdot 	ext{m}}{0.125} = 96 	ext{ kg}$$Therefore, the mass of the disk is 96 kg.

A Torque of 12 N ∙ M Is Applied to a Solid,uniform