IB Physics: Uniform Circular Motion

IB Physics: Uniform Circular Motion

Uniform Circular Motion

1.Draw a vector diagram to illustrate that the acceleration of a particle moving with constant speed in a circle is directed towards the centre of the circle

The below image will be very important, so make sure you understand it. Note that all quantities below are denoted as vectors.

The object going in a circular motion is said to be going through uniform circular motion . Since the object is moving, it has a velocity.

The speed, which is a scalar quantity which does not depend on the direction of the object, remains constant. However, if you look above, the direction of velocity vectors are constantly changing – and since velocity is a vector quantity, and vectors depend on both the speed and direction, velocity is constantly changing.

To sum this up:

• In UCM (Uniform Circular Motion) , speed is constant.
• However, velocity (a vector quantity), is constantly changing.

As we can see, as the velocity is constantly changing, there’s an acceleration.

A key factor you need to know about the acceleration is that it’s centripetal, or in other words “center seeking”. The direction of the acceleration will always be directed towards the center of the circle, and is perpendicular (at 90 degree angles) to the velocity vector. A visual representation of this can be seen in the above diagram.

Exam tip: This comes up quite often, ‘What is the work done during Uniform Circular Motion?’. The answer is zero.

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Work is basically when a force on an object causes a displacement in the direction of the force – as in uniform circular motion, the displacement is always perpendicular to the direction of the force, work done is zero.

Additionally, the “w” like symbol you see in the circle is actually called omega, and this is a measure of the Angular velocity of the object – you know how there’s 2π radians in a circle (if you don’t, get a high-school trigonometry book out). Angular velocity is simply a measure of the amount of radians the object sweeps out per unit time. If we want to model this mathematically, we arrive at:

T = period (this is the amount of time required for one revolution)

If we want to relate this with velocity, we can take this approach:

Since v = d/t

d, distance here is the circumference of the circle , which is 2πr. Time taken ,t, is T, the period.

So, the formula goes:

Expression for centripetal acceleration:

Centripetal acceleration is calculated using the formula:

ac = v2/r

Centripetal means “center seeking” – the acceleration always seeks the center of the circular object.

Force producing circular motion in various situations.

This acceleration is caused by a force which according to Newton’s Second Law , F= ma. We call this the centripetal force. This force is literally what keeps the body moving at a uniform speed along the circular path.

Examples:

• Artificial satellites moving in circular motion around the earth.
• Frictional forces between tyres and the road.
• Multiple choices love asking for examples of uniform circular motions, and the second one comes up very often, mostly because it’s not very obvious.