Question

A disk of a radius 50 cm rotates at a constant rate of 100 rpm. What distance in meters will a point on the outside rim travel during 30 seconds of rotation? ​
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Answer 1

Answer:

A point on the outside rim will travel 157.2 meters during 30 seconds of rotation.

                         

Explanation:

We can find the distance with the following equation since the acceleration is cero (the disk rotates at a constant rate):

$d = v*t$

Where:

v: is the tangential speed of the disk

t: is the time = 30 s  

The tangential speed can be found as follows:

$v = \omega*r$

Where:

ω: is the angular speed = 100 rpm

r: is the radius = 50 cm = 0.50 m

$v = \omega*r = 100 \frac{rev}{min}*\frac{2\pi rad}{1 rev}*\frac{1 min}{60 s}*0.50 m = 5.24 m/s$    

Now, the distance traveled by the disk is:

$d = v*t = 5.24 m/s*30 s = 157.2 m$

Therefore, a point on the outside rim will travel 157.2 meters during 30 seconds of rotation.

I hope it helps you!