# Relationship between Angular Acceleration & Linear Acceleration

### 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 = r*θ*

Let r = A = radius of the circle.

The angular velocity (ω) is given by:

You are viewing an excerpt of this Topic. Subscribe Now to get **Full Access** to **ALL** this Subject's Topics and Quizzes for this Term!

Click on the button **"Subscribe Now"** below for Full Access!

### Subscribe Now

**Note:** If you have **Already Subscribed** and you are seeing this message, it means you are logged out. Please **Log In** using the **Login Button Below** to **Carry on Studying!
**

Thank you 😊