A particular motor can provide a maximum torque of 110 N ? m. Assuming that all of this torque is used to accelerate a solid, uniform, cylindrical flywheel of mass 10.0 kg and radius 3.00 m, how long will it take for the flywheel to accelerate from rest to $8.13 \mathrm { rad } / \mathrm { s } ?$
A)3.33 s
B)2.83 s
C)4.03 s
D)4.36 s

Question

Quizplus · Accepted Answer

Explanation:The torque on the flywheel is:$$\tau = I \alpha$$where I is the moment of inertia of the flywheel and \alpha is the angular acceleration. The moment of inertia of a solid, uniform, cylindrical flywheel is:$$I = \frac{1}{2}MR^2$$where M is the mass of the flywheel and R is its radius. Substituting into the first equation, we get:$$\tau = \frac{1}{2}MR^2 \alpha$$Solving for \alpha, we get:$$\alpha = \frac{2\tau}{MR^2}$$The angular acceleration is constant, so we can use the following equation to find the time it takes for the flywheel to accelerate from rest to $8.13 \mathrm { rad } / \mathrm { s } $:$$\omega_f = \omega_i + \alpha t$$where $\omega_i$ is the initial angular velocity, $\omega_f$ is the final angular velocity, and t is the time. Substituting in the values we know, we get:$$8.13 \mathrm { rad } / \mathrm { s } = 0 + \frac{2(110 \mathrm { N } \cdot \mathrm { m })}{(10.0 \mathrm { kg })(3.00 \mathrm { m })^2} t$$Solving for t, we get:$$t = 3.33 \mathrm { s }$$

A Particular Motor Can Provide a Maximum Torque of 110 8.13rad/s?8.13 \mathrm { rad } / \mathrm { s } ?8.13rad/s?

A Particular Motor Can Provide a Maximum Torque of 110 $8.13 \mathrm { rad } / \mathrm { s } ?$