Video Transcript
In a hard disk drive, a constant
torque of 14.0 newton meters is applied to the magnetic disk when the drive starts
recording data. The magnetic disk has a moment of
inertia of 1.12 kilogram meters squared. What is the magnitude of the
angular acceleration of the disk?
We can draw a diagram that
represents the disk rotating with the information provided from the problem. In our diagram, we have labeled the
magnitude of the torque applied to be 14.0 newton meters, the moment of inertia of
the disk to be 1.12 kilogram meters squared, and we are solving for our angular
acceleration 𝛼.
To solve the problem at hand, we
needed an equation that relates these three variables together. Newton’s second law of motion when
applied to rotational motion is the net torque, 𝜏 net, is equal to the moment of
inertia of the object, 𝐼, times the angular acceleration of the object, 𝛼. The problem asks us to solve for
the angular acceleration. However, our equation right now is
written in the form that it’s solving for torque. Therefore, we must rearrange our
formula to solve for 𝛼.
To isolate 𝛼, we must divide both
sides of the equation by 𝐼, canceling out 𝐼 from the right side of the equation,
leaving us with torque divided by moment of inertia is angular acceleration. Substituting in our values, we have
14.0 newton meters for our torque and 1.12 kilograms meters squared for our moment
of inertia. When we divide these two numbers,
we get an angular acceleration of 12.5 radians per second squared. The magnitude of the angular
acceleration of the disk is 12.5 radians per second squared.
