Question

a hamster running in a wheel of radius 13 cm spins the wheel one revolution in 4 seconds.
a) what is the angular velocity of the wheel? (in radians/sec)
select an answer

b) at what linear velocity is the hamster running? (in cm/sec)
select an answer

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Explanation:

Step1: Find the angular velocity

The formula for angular velocity \(\omega\) is \(\omega=\frac{\theta}{t}\). One revolution is \(\theta = 2\pi\) radians and \(t = 4\) seconds.
\(\omega=\frac{2\pi}{4}=\frac{\pi}{2}\text{ rad/sec}\)

Step2: Find the linear velocity

The formula for linear velocity \(v\) is \(v = r\omega\), where \(r = 13\) cm and \(\omega=\frac{\pi}{2}\text{ rad/sec}\)
\(v=13\times\frac{\pi}{2}=\frac{13\pi}{2}\approx 20.42\text{ cm/sec}\)

Answer:

a) \(\frac{\pi}{2}\)
b) \(\frac{13\pi}{2}\approx 20.42\)