Question

A computer hard disk starts from rest, then speeds up with an angular acceleration of 190rad/s2 until it reaches its final angular speed of 7200 rpm.
How many revolutions has the disk made 10.0 s after it starts up?

Answer 1

have you attempted this question?

Answer 2

Remember that the kinematics for rotational motion closely resemble the kinematics for linear motion

just like displacement (s) and velocity (v) with linear kinematics
\[s=v_it+\frac{1}{2}t^2\]
\[s=vt\]
and
\[v=at\]
for rotational motion, the angular displacement (θ) (number of radians traveled through) and angular velocity (ω) are given by
\[ \theta = \omega_i t + \frac{1}{2}\alpha t^2\]
\[\theta = \omega t\]
and
\[\omega=\alpha t\]
Where alpha is the angular acceleration, and omega is the angular velocity.

You need to find out how long it takes for the hard disk to reach a constant angular velocity, then add the angular displacement during acceleration to the angular displacement while it's angular velocity is constant (***hint: if it even reaches max speed in 10 seconds).

You also need to remember that the angular displacement theta has to be converted into revolutions from radians
\[1 \ \text{rev} = 2\pi \ \text{rad}\]