# A child on a barber shop spins on a stool. If the child turns counterclockwise through 8.0 radians at a certain time and with an angular velocity of 2.56 rad/s. What is the time interval in minutes when the child turns?

## 8.0 rad / (2.56 rad/s) = 8.0/2.56 = 3.125 s

Now convert that to minutes...

## Well, this child seems to be having a "spinning" good time! Let's calculate the time interval in minutes so we can keep track of all the giggles.

To find the time interval, we can use the formula: time = angle / angular velocity.

Given that the child turns counterclockwise through 8.0 radians and has an angular velocity of 2.56 rad/s, we can plug these values into the formula:

time = 8.0 radians / 2.56 rad/s

Calculating this, we find that the time is approximately 3.125 seconds.

But hey, you asked for the time interval in minutes! No worries, I've got you covered.

To convert seconds to minutes, we divide the time by 60 (since there are 60 seconds in a minute):

time in minutes = 3.125 seconds / 60

After crunching the numbers, we get the time interval to be approximately 0.0521 minutes.

So, the child took approximately 0.0521 minutes to complete the spin.

I hope that brings a smile to your face, just like a spinning child at a barber shop!

## To find the time interval in minutes when the child turns counterclockwise through 8.0 radians, we can use the formula:

time = angle / angular velocity

Given:

Angle = 8.0 radians

Angular velocity = 2.56 rad/s

Substituting the given values into the formula, we have:

time = 8.0 rad / 2.56 rad/s

Simplifying the expression:

time = 3.125 s

Since we want the answer in minutes, we need to convert seconds to minutes:

time = 3.125 s * (1 min / 60 s)

Simplifying the expression:

time = 0.0521 min

Therefore, the time interval when the child turns counterclockwise through 8.0 radians is approximately 0.0521 minutes.

## To calculate the time interval in minutes when the child turns, we need to use the formula for angular displacement. Here's how we can do it step by step:

1. The child turns counterclockwise through 8.0 radians. This is the angular displacement (θ) of the child.

2. The angular velocity (ω) of the child is given as 2.56 rad/s.

3. The formula to calculate the time interval (t) is t = θ / ω.

Plugging the values into the formula, we have:

t = 8.0 radians / 2.56 rad/s

Now, let's calculate the time interval:

t = 8.0 / 2.56

Dividing 8.0 by 2.56, we get:

t ≈ 3.13 seconds

Since we want the time interval in minutes, we need to convert seconds to minutes. There are 60 seconds in a minute, so:

t ≈ 3.13 seconds * (1 minute / 60 seconds)

Simplifying, we get:

t ≈ 0.0522 minutes

Therefore, the time interval in minutes when the child turns counterclockwise through 8.0 radians with an angular velocity of 2.56 rad/s is approximately 0.0522 minutes.