Lesson 8, Topic 1
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# Relationship between Angular Acceleration & Linear Acceleration

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### Topic Content:

• Speed
• Acceleration
• Relationship between Angular Acceleration & Linear Acceleration
• Summary

### Speed:

From the diagram, as the particle P moves round the circle once it sweeps through an angle = 360º. Where 360º = 2π radians, in time T seconds.

The time rate of change of angle with time (t) is called the angular velocity (ω).

ω = $$\frac{angle \: turned \: through \: the \: body}{time \: taken}$$

ω = $$\frac{θ}{t}$$

∴ θ = ωt

This is similar to:
distance = velocity × time

s = v × t

∴ v = $$\frac{s}{t}$$ for linear motion;

The angle θ is measured in radians
since, 2π rad = 360º
from, ω = $$\frac{θ}{t}$$
angular velocity is measured in radians per second (rad/s)

When θ changes with time, the length of the arc PZ = s, also changes with time.

By definition, θ in radians = $$\frac{s}{r}$$

s = rθ

Let r = A = radius of the circle.

The angular velocity (ω) is given by:

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