Question

A coin had 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

Answer 1

It would travel 1800 millimeters in 0.125 seconds, which requires a rotation of 180° at 4 revolutions per second.

Explanation:

The given angle is 180°, the given velocity is 4 revolutions per second.

We know that the circumference of a circle is
`2\pi`, one revolution is equal to 360°, which means the given angle represents half of a revolution.

Also, we know by given that the radius of the coin is 10 mm, which give a length of

`L= 2\pi r= 2 \pi (10mm)=20 \pi mm`

If the whole length of the coin is
`20 \pi mm`, then it would take
`10 \pi \ mm` to travel 180°.

Assuming that it's a constant movement, we have

`\theta = \omega t`

Where
`\thetta = 180\°`,
`\omega = 4 \ rev/sec \implies \omega = 4(360) \°/sec=1,440`

`180=1,440t\\t=(180)/(1,440) \approx 0.125 \ sec`

Therefore, it would take 0.125 seconds to travel 180° with a velocity of 4 revolutions per second.

To know how far travels during this time, we use the following formula

`s =\theta r\\s= 180 * 10\\s=1800 mm`

Therefore, it would travel 1800 millimeters in 0.125 seconds, which requires a rotation of 180° at 4 revolutions per second.

Answer 2

A coin has a radius of 10 mm. How long will it take the coin to roll through the given angle measure at the

glven angular velocity? How far will it travel in that time? Round to the nearest tenth.

180°; 2 rev/sec

The coin will take

sec to roll 180° and travels approximately

mm.

Explanation:

Given that,

The angle is 180°

Angular velocity is 2rev/sec

The radius is 10mm

we are to find the time and distance traveled at that time

The formula is

θ = at

where t is the time,

a is the angular velocity

θ is angle in radian

so,

θ = 180° × π/180°

θ = π

= 3.14

Hence ,

θ = at

3.14 = 2t

t = 1.57sec

let the distance be xmm

`(1.57 * 180^0)/(360) = (x)/(20 \pi) \\\\0.785 = (x)/(20 \pi) \\\\x = 49.32mm`

Therefore , the time is 1.57 sec and the distance is 49.32mm