Lesson 6, Topic 5
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# Angular Speed and Velocity

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### Topic Content:

• Angular Speed and Velocity

When a stone is tied to the end of a string or rope and whirled around, the stone moves in a circular path as shown in the diagram below.

Suppose that as the stone is being whirled around, it moves from point M to N, in t seconds, so that the radius OM sweeps through an angle Î¸ at the same time.

As the stone moves around the circular path and sweeps through angle Î¸, the stone moves with angular velocity, $$\scriptsize \omega$$

Angle $$\scriptsize \hat{MON} = \theta ,$$ the angular velocity of motion, $$\scriptsize \omega$$ can be defined as;

$$\scriptsize \omega = \normalsize \frac{\theta}{t}$$ ……………..(1)

We can say that the angular velocity, $$\scriptsize \omega ,$$ is the angle turned through, with respect to time.

Recall that linear velocity, v is given by the formula:

$$\scriptsize v = \normalsize \frac{s}{t}$$ …………….(2)

where s is the length of the arc MN.

Comparing equations 1 and 2, instead of using linear displacement in 1, we used angular displacement Î¸.

The image illustrates the relationship between the radius and the central angle Î¸ in radians.

We define the rotation angle Î¸ to be the ratio of the arc length to the radius of curvature:

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1. thank you