#### Gravity and Motion

#### Physics (Year 12)

Circular motion can be uniform; meaning it can either have a constant rate of rotation throughout the duration of its motion, or it can be non-uniform, meaning its rate of rotation can vary. This course only considers and tests students upon uniform circular motion.

There are 3 forms of circular motion; horizontal, banked, vertical. Here we will discuss horizontal circular motion and introduce some new equations that will be used in every form of circular motion question (horizontal, banked, or vertical).

Examples of horizontal circular motion include: a car going around a roundabout, planets revolving around the sun, a spinning wheel.

# Causes of Circular Motion

For an object to be in circular motion, it needs to be continuously accelerating towards the centre of its circular path. If we recall Newton’s second law of motion, we know that for an object to accelerate, there needs to be a net unbalanced force continuously acting on the object. The force that causes an object to continue to accelerate towards the centre of its circular path is known as the centripetal force, and so the acceleration experienced due to this is known as the centripetal acceleration.

Centripetal force can be provided by: friction between a car’s tyres and the road, the tension force in a cable which is spinning a rock around, gravitational attraction of the Earth towards the Sun, or simply the normal force from a wall.

# Equations

For every form of circular motion, the velocity of the object at any instant is tangential to its path. For an object in circular motion, the direction of its velocity is constantly changing, hence in circular motion calculations, we focus on the average speed of the object.

The average speed of an object moving in a circular path is given by:

T, the period is time required once around the circular path. Related to the period is frequency, f, which is the number of rotations around the circular path each second. Period is the inverse of frequency, and vice versa.

Centripetal acceleration, which always directed at the centre of the circular path, is given by:

Using the equation for velocity that we learnt earlier, the equation for centripetal acceleration can be re-written as:

Applying Newton’s second law of motion (F = ma), we can derive the equation for centripetal force:

If this centripetal force disappears, then the object will continue to move in a straight line tangential to its circular path because velocity is tangential to its circular path and there is no force causing the ball to change direction.

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