# Thread: Motion on a Circle

1. ## Motion on a Circle

An object is traveling around a circle with a radius of 2 meters. If in 20 seconds the object travels 5 meters, what is its angular speed? What is its linear speed?

Also: What is the basic difference between angular and linear speed?

2. Originally Posted by magentarita
An object is traveling around a circle with a radius of 2 meters. If in 20 seconds the object travels 5 meters, what is its angular speed? What is its linear speed?

Also: What is the basic difference between angular and linear speed?
The linear speed:
$\displaystyle v = \frac{d}{t}$

Where:
• $\displaystyle v =$ Linear speed
• $\displaystyle d =$ Distance travelled
• $\displaystyle t =$ Time (in which the distance is travelled)

$\displaystyle v = \frac{d}{t}$
$\displaystyle v = \frac{5}{20}$
$\displaystyle v = \frac14\text{ ms}^{-1}$

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Angular speed:
$\displaystyle v = r\omega$

Where:
• $\displaystyle v$ = Linear speed
• $\displaystyle r$ = Radius
• $\displaystyle \omega$ = Angular speed (In radian)

$\displaystyle v = r\omega$
$\displaystyle \frac14 = 2 \omega$
$\displaystyle \omega = \left(\frac14\right) \div 2$
$\displaystyle \omega = \frac18\text{ rads}^{-1}$

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The Difference:
Linear velocity is a change of speed in a straight line. Angular speed is the rate of change of angle with respect to time. These two are convertible in a case of a circle motion. In a circle, across a tangent, linear speed can be measured and across the arc traveled, angular speed can be measured.

3. ## Great

A wonderful explanation!