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Notes by Category University Engineering

Mechanics & Stress Analysis*
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  • A-Level Physics

Circular Motion, SHM & Oscillations

The S.I. unit for angles is not degrees, but radians. This is the angle subtended by a circular arc with a length equal to the radius of the circle:

radians diagram. EngineeringNotes Engineering Notes

1 rad is equal to about 57.3°

There are 2π in a circle, and half that in a semicircle. Therefore,

  • to convert from degrees to radians, divide the angle in degrees by 180/π

  • to convert from radians to degrees, multiply the angle in radians by 180/π

Circular Motion

While the velocity of linear motion is defined as displacement / time, the velocity of circular motion is defined as angle / time. Therefore, it is called angular velocity, and is given the Greek letter omega, ω.

ω = θ/t angular velocity = angle / time

This equation is rarely used, however, as it is far easier to work with the time period and frequency of circular motion.

  • Time period, T, is the time taken for it to complete one circle.

  • Frequency, f, refers to the number of complete rotations (of 2π rads) per second.

This gives rise to the far more helpful equations:

ω = 2π/T angular velocity = 2π / time period
ω = 2πf angular velocity = 2π x frequency

The units of angular velocity are radians per second.

We can calculate the linear velocity using the angular velocity:

v = ωr linear velocity = angular velocity x radius

Centripetal Force

Even if the object undergoing circular motion is travelling at a constant speed, its velocity is always changing (due to its direction changing). This means the object is always accelerating – this is known as centripetal acceleration, and always acts towards the centre of the circle.

a = v²/r centripetal acceleration = linear velocity² / radius
a = ω²r centripetal acceleration = angular velocity² x radius