StemUp: OCR A A level Physics 5.2: Circular motion

What is a radian and how can it be used to measure angles? (3)

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

- To convert from radians to degrees, multiply by 180 and divide by π

- To convert from degrees to radians, divide by 180 and multiply by 2π

What is meant by the period in circular motion? (1)

This is the time in seconds for an object to travel a full circle.

What is meant by the frequency in circular motion? (1)

The frequency is the number of full circles travelled by an object in one second. It is measured in Hertz (Hz).

What is the relation between the period and frequency? (1)

The two are related by the formula: f = 1 / T​

What is meant by the angular velocity in circular motion? (1)

This is the rate of change of angle for an object moving in a circle.

What is the formula for the angular velocity? (1)

This is given by: ω = θ / t

​Where θ is the angle travelled by the object (in radians) and t is the time (s) the object travelled in a circle for.

What is the unit for angular velocity? (1)

Angular velocity is measured in rads^-1

How can the formula for angular velocity be written in terms of period and frequency? (2)

- In a time of one period (T) the object will travel a full circle of 2π radians.

- The angular velocity can therefore be written as: ω = 2π \ T or ω = 2πf as f = 1/T

What is meant by a centripetal force? (3)

- As the direction of an object moving in a circle is constantly changing, the velocity and acceleration is also changing as they are vector quantities.

- The acceleration is provided by the centripetal force.

- Centripetal force is the net force which acts perpendicular to the direction of velocity, pointing towards the centre of the circle.

Why does the velocity and acceleration change when an object moves at constant speed in a circle? (1)

As the direction of an object moving in a circle is constantly changing, the velocity and acceleration is also changing as they are vector quantities.

What is the equation for the speed of an object moving in a circle? (1)

The speed is given by: v = 2πr / T = ωr​

What is the equation for the centripetal acceleration of an object? (2)

- The centripetal acceleration is given by: a = v^2 / r

- As v = ωr this can be rewritten as: a = ω^2 r

What is the equation for the centripetal force of an object? (2)

As F = ma from Newton's second law the centripetal force is given by:

- F = mv^2 / r

- F = mω^2 r as v = rω

How can circular motion be investigated using a whirling bung? (5)

- Attach a bung with mass m to a string and put it through a glass tube.

- Rotate the string in a circle and calculate the time taken for 1 revolution and use this as the period to calculate the angular velocity. Also measure the radius of the rotating string.

- Equate the centripetal force to the weight as the weight provides the centripetal force to give: mg = mω^2 r

- Use this to find the speed on the bung as v = rω

- When v^2 is plotted against mass, a straight line through the origin should be found as they are directly proportional to each other.