Circular motion

How is the radian defined

A radian is the angle subtended by a circular arc with a length equal to the radius of the circle

angle in radians = arc length/radius

how many radians are in 360 degrees

2π radians

how do you convert from degrees to radians

multiply by π/180

how do you convert from radians to degrees

multiply by 180/π

How is angular velocity defined, equation and units

We define angular velocity 𝜔 as the rate of change of an angle.

ω = θ/t = 2π/T

Angular velocity's units are rad/s

what is meant by time period T in circular motion?

In a time t equal to one period T the object will move through an angle θ equal to 2π radians

Explain why an object travelling in a circle at a constant speed is accelerating

When you move a circular path, your direction is constantly changing. As a result your velocity is changing even if you travel at a constant speed. This change in velocity means that objects following a circular path must be accelerating and the greater the rate of change of velocity the greater the acceleration

what is centripetal acceleration? Give an explanation and the direction it acts

The acceleration of any object travelling in a circular path at constant speed. Always acts towards the centre of the circle

What direction does centripetal force act?

Any object travelling in a circular path must have a resultant force acting on it at right angles to its velocity

Describe an experiment that can be performed to investigate circular motion

A whirling bung on a string can be used as part of a simple investigation into centripetal force

As the bung is swung in a horizontal circle the suspended weight remains stationary as long as the force it provides (Mg) is equal to the centripetal force required to make the bung travel in the circular path. If the centripetal force required is greater than the weight then the weight moves upwards.

The weight and thus the centripetal force required for different masses, radii and speeds can then be investigated

define the newton

the force that causes a mass of 1kg to have an acceleration of 1ms^-2