# 6.1.3 Angular Speed

### Angular Speed

• Any object travelling in a uniform circular motion at the same speed travels with a constantly changing velocity
• This is because it is constantly changing direction, and is therefore accelerating
• The angular speed (⍵) of a body in circular motion is defined as:

The rate of change in angular displacement with respect to time

• Where:
• Δθ = change in angular displacement (radians )
• Δt = time interval (s)
• Angular speed is a scalar quantity, and is measured in rad s-1

When an object is in uniform circular motion, velocity constantly changes direction, but the speed stays the same

• Taking the angular displacement of a complete cycle as 2π, the angular speed ⍵ can be calculated using the equation:

• Where:
• v = linear speed (m s-1)
• r = radius of orbit (m)
• T = the time period (s)
• f = frequency (Hz)
• Angular velocity is the same as angular speed, but it is a vector quantity
• This equation tells us:
• The greater the rotation angle θ in a given amount of time, the greater the angular velocity ⍵
• An object rotating further from the centre of the circle (larger r) moves with a faster angular velocity (larger ⍵)

#### Worked Example

A bird flies in a horizontal circle with an angular speed of 5.25 rad s-1 of radius 650 m.

Calculate:
a) The linear speed of the bird
b) The frequency of the bird flying in a complete circle

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