# Question #5771d

Jul 4, 2015

The bug's tangential acceleration is $\frac{13 \pi}{3}$cm/sec²$\approx 13.6$cm/sec²

#### Explanation:

Acceleration is defined as "the variation of speed with respect to time"

We know that the disk we are working with goes from rest (0rev/s) to an angular speed of 78rev/min within 3.0s.

The first thing to do is convert all the values to the same units:

We have a disk with a 10cm diameter, that takes 3.0s to go from rest to 78rev/min.
One revolution is as long as the disk's perimeter, that is:
$d = 10 \pi c m$
One minute is 60 seconds, therfore the final angular speed is:
78rev/min = 78rev/60sec = $\frac{78}{60}$rev/sec = 1.3rev/sec.

We now know that, after three seconds, every point of the rim of the disk is fast enough to travel 1.3 times the disk's perimeter in one second, that is:

1.3rev/sec = 1.3*d/sec = $13 \pi$cm/sec

Since it took the disk 3.0s to go from rest to this speed, we can calculate that the acceleration of every point of the rim of the disk (and thus of a bug standing on the rim of the disk) is:

$\left(\text{amount of speed gained")/("time passed}\right) = \frac{13 \pi}{3.0}$cm/sec²$\approx 13.6$cm/sec²