Question

A wheel with a 30-cm radius is rotating at a rate of 3 radians/sec. What is the linear speed of a point on its rim, in meters per minute?

Solution

Verified

Use the formula relating the linear speed $v$ and angular speed $\omega$:

$v=\omega r$

where $r$ is the radius.



Substitute $\omega=3$ radians/sec and $r=30$ cm:

$v=(3\text{ rad/s})(30\text{ cm})$

$v=90\text{ cm/s}$

Convert to m/min:

$v=\dfrac{90\text{ cm}}{\text{s}}\times \dfrac{1\text{ m}}{100\text{ cm}}\times \dfrac{60\text{ s}}{1\text{ min}}=\color{#c34632}54\text{ m/min}$

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