An 8.0-cm radius disk with a rotational inertia of 0.12 kg .0 m² is free to rotate on a horizontal axis. A string is fastened to the surface of the disk and a 10-kg mass hangs from the other end. The mass is raised by using a crank to apply a 9.0-N.m torque to the disk. The acceleration of the mass is: A) 0.50 m/s² B) 1.7 m/s² C) 6.2 m/s² D) 12 m/s² E) 20 m/s²

Question

Quizplus · Accepted Answer

The torque applied to the disk is equal to the product of the force applied and the radius of the disk. The rotational inertia of the disk is equal to the mass of the disk multiplied by the square of its radius. The acceleration of the mass is equal to the torque applied to the disk divided by the rotational inertia of the disk.$$a = \frac{	au}{I} = \frac{Fr}{I} = \frac{(9.0 	ext{ N})(0.080 	ext{ m})}{0.12 	ext{ kg m}^2} = 6.0 	ext{ m/s}^2$$

An 80-Cm Radius Disk with a Rotational Inertia of 0