A hard drive with a spin speed of 7200 RPM, commences spinning at time = 0, at time = 1.326 ms what is the angle that the disk has rotated by relative to it's start position?

I. In degrees

II. In Radians

Answer: I. 57º 17' II. 1 rad.

Explanation:

A spin speed, implies the relationship between the angle rotated and the time that has been spinning, which is equal, by definition, to the angular velocity.

ω = Δ∅ / Δt

In order to get the angle rotated in degrees, we need to convert first from RPM (revolutions per minute) to º/sec, as follows:

7200 rev/min * (1 min/60 sec) * (360º / 1 rev) = 7200 * 6 = 43200 º/s

Now, we know that the time passed since it started to spin, was 1.326 msec, i. e., 0.001326 sec.

Remembering that ω = Δ∅ / Δt, solving for Δ∅, we get:

Δ∅ = 43200 º / s * 0.001326 sec = 57º 17'

II. In order to get the answer in rads, we can convert the rpm to rads/sec, as follows:

7200 rev/min * (1 min/60 sec) * (2 π / 1 rev) = 240 π rad/sec.

Applying the same equation as above, we get:

Δ∅ = 240 π rad/s * 0.001326 sec = 1 rad.