Question

A coin has a radius of 10 mm. How long will it take the coin to roll through the given angle measure at the given angular velocity? How far will it travel in that time? Round to the nearest tenth.

540°; 6 rev/sec

The coin will take
sec to roll 540° and travels approximately
mm.

Answer 1

t = 1.57 sec

distance, d = 98.65 mm

Explanation:

Given an angle of 540°

At 6 revolutions per second, which is the angular velocity.

Radius, r = 10 mm

We are asked to find the time and the distance.

To find the time, let's use the formula:

`\theta = a*t`

Where
`\theta` = angle in radians.

Converting 540° to radians, we have:

`\theta = 540 * (\pi)/(180) = 9.42 rad`

Therefore, from the formula, let's find t.

`\theta = a*t`

`9.42 = 6 * t`

`t = (9.42)/(6) = 1.57`

time = 1.57

To find the distance, we have:

`(1.57 * 360)/(360) = (d)/(2 \pi r)`

`(1.57 * 360)/(360) = (d)/(2\pi 10)`

`1.57 = (d)/(20\pi)`

`d = 20 \pi *1.57`

d = 98.65 mm

Therefore, the time is 1.57 seconds and the distance is 98.65 mm