A uniform solid disk of mass and radius starts from rest and is subjected to a…
PHYSICS · Multi-part · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion
Problem
A uniform solid disk of mass 5.0kg and radius 0.40m starts from rest and is subjected to a constant net torque that produces an angular acceleration of 4.0rads−2. The disk rotates about its central axis, and its center of mass remains stationary throughout the motion.
(a) Derive an expression for the disk’s angular speed ω(t) as a function of time t during the period of constant angular acceleration, stating any kinematic relationships you use.
(b) Using your result from part (a), obtain a symbolic expression for the disk’s rotational kinetic energy K(t) as a function of time.
(c) Calculate the rotational kinetic energy of the disk after it has been accelerating for 3.0s.
(d) Discuss how the rate at which the rotational kinetic energy increases with time compares to the rate at which the angular speed increases with time for this uniformly accelerated rotation.