Question

a hamster runs at a speed of 20 centimeters per second in a wheel of radius 11 centimeters.
a) what is the angular velocity of the wheel? (in radians/sec)
select an answer

b) how fast will the wheel spin in revolutions per minute?

Explanation:

Step1: Find angular velocity

The formula for linear velocity \(v = r\omega\), where \(v\) is linear velocity, \(r\) is radius and \(\omega\) is angular velocity.
Given \(v = 20\) cm/s and \(r=11\) cm.
We can solve for \(\omega\) by \(\omega=\frac{v}{r}\).
Substitute the values: \(\omega=\frac{20}{11}\approx1.82\) radians/sec.

Step2: Convert angular velocity to revolutions per minute

We know that \(1\) revolution \( = 2\pi\) radians and \(1\) minute \(=60\) seconds.
First, we have \(\omega=\frac{20}{11}\) radians/sec.
To convert to revolutions per minute:

$$
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$$

Answer:

a) \(\frac{20}{11}\approx1.82\) radians/sec
b) \(\frac{600}{11\pi}\approx17.3\) revolutions per minute