Question

A coin completes 18 spins in 12 seconds. The centripetal acceleration of the edge of the coin is 2.2 m/s2. The radius of the coin is ____-blank

Answer 1

Answer: 0.025 m or 2.5m

Explanation:

The number of spins given in 12 seconds = 18

So the number of spins in 1 second will be

= 18 / 12 = 1.5rps

The above result is the frequency because it is the number of spins in one second

Let f be frequency

f = 1.5 rps

Using centripetal acceleration given

Ca = 2.2 m/s^2

m is the radius of the given coin

Using the formula

Centripetal acceleration, = m x w^2

Knowing that w = 2πf

2.2 = m x ( 2 x 3.14 x 1.5) ^2

2.2 = m x 88.7364

m = 0.025 m

Answer 2

0.025 m

Step-by-step explanation:

The coin completes 18 revolutions in 12 seconds. The angular velocity of the coin is:

`\omega = (18 rev)/(12 s) \cdot (2\pi (rad)/(rev))=9.42 rad/s`

The centripetal acceleration of the edge of the coin is given by

`a=\omega^2 r`

where we have

a = 2.2 m/s^2 is the acceleration

r is the radius of the coin

Solving for r, we find

`r=(a)/(\omega^2)=(2.2 m/s^2)/((9.42 rad/s^2)^2)=0.025 m`