A solid disk with a radius of #1 m# and mass of #2 kg# is rotating on a frictionless surface. If #36 W# of power is used to increase the disk's rate of rotation, what torque is applied when the disk is rotating at #3 Hz#?
In linear motion, we might define power,
Now, because work is defined by a force applied across some distance (provided there is no angle the force is applied at which would alter the calculation, i.e.
Units for power are given in watts, where a watt is the equivalent of joules per second.
Linear motion and rotational motion are analogous to each other. Where in linear motion we speak in terms of forces, masses, and velocities, in rotational motion we talk about torques, moments of inertia, and angular velocities, respectively. We can rewrite our equation for power (derived above) in terms of torque and angular velocity.
Using the given values of
Solving our power equation for
And, using our values for