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

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

Step-by-step 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 (rev)/(min)*(2\pi rad)/(1 rev)*(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!