Ever wondered why the wheels on a car appear to rotate backwards when you see a video of it going extremely fast? My friend, this is due to circular motion and the frames per second of the video. After today’s lesson you will understand uniform circular motion and will have seen Circular motion HSC Questions.

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**Learning intentions**

*Understand what uniform circular motion is and how to model it with mathematical queations**Analyse the total energy and work done on an object executing uniform circular motion**Know and understand how to use these equations*:

What is circular motion?

Circular motion is about describing motion when an object is following the path of a circle. For example, when you drive around a round-a-bout, you are undertaking circular motion. Assuming you tangential velocity isn’t changing – meaning you speedometer is saying you are going the same speed the entire time – you are in uniform circular motion.

Another example is the motion of the earth around the sun. We can say this is uniform circular motion.

What is the difference between tangential velocity and angular velocity?

Angular velocity is the change in the angle over time. Tangential velocity is the change in distance over time. What this means is that dots A and B on a rotating plate will have the same angular velocity since they are sweeping the same angle over time. In other words, they will take the same amount of time to rotate one revolution.

Whereas, their linear velocities would be significantly different. Point B is Further away from the centre of the record player hence it will have a larger linear velocity then point A. Since the total distance travelled in one revolution is greater.

**Figure 1.** A record player rotating with two dots, A and B, on it.

This then gets us onto how to model these two concepts mathematically. If we are thinking about the turntable in figure 1, this is very easy to do.

**Angular velocity**

For angular velocity, it will be the change in the angle over time.

Change in angle is measured in radians so in figure 1, if the turntable takes 5 seconds to complete 1 revolution. Then the angular velocity for both A and B would be 2*pi/ 5 radians per second.

**Tangential velocity**

For the tangential velocity, it will be the change in distance covered over time.

Change in distance is going to be based on the circumference travelled, and the time taken will be the time taken to complete one revolution, which is the period.

So lets say in figure 1, point A is 2 cm away from the centre and point B is 8 cm away from the centre.

What factors affect circular motion velocity?

When we talk about circular motion, we want to consider what factors will affect the objects velocity.

The only way to increase angular velocity is to shorten the time for the object to make one revolution.

However, increasing the tangential velocity can be done two ways. Either we increase the radius (the distance of the object from the centre of rotation) or we shorten the time for the object to make one revolution.

Ok, I get circular motion, but where does acceleration and force come into it?

Remember learning that acceleration occurs when there is a change in speed or direction of an object. Well, uniform circular motion is a type of acceleration since the direction of the object is changing even if the speed isn’t changing.

The centripetal acceleration can be calculated by squaring the tangential velocity and dividing by the radius.

Knowing then, F=ma, substitute centripetal acceleration

This force is applied perpendicular to the tangential velocity, which means it is pointing towards the centre of the circular path the object is following.

Lets understand how this relates to total energy and work done

The strange thing with circular motion is the work done will be 0 if we start where we finish – i.e. we make one full revolution.

## Circular Motion HSC Questions

*Well done for reaching here, you know the secret to success is doing exam-style questions and marking your answers. To get the most from this make sure you do the question before you check the answers – this way you can make the most of active recall and truly make the lesson stick.*

**Question 1.**

Two identical coins are placed on a record player, one is placed near the outer edge, 8 cm from the centre of the record player while the other is placed only 2 cm from the centre of the rotating record. The time taken for one rotation of the record player is 3 seconds. Analyse the angular and tangential velocity to predict which coin is more likely to fly off. [3 marks]

**Question 2.**

A car is turning around a roundabout, they take 15 seconds to travel half-way around the roundabout. What is their angular velocity? [1 mark]

**Question 3.**

A car is turning around a roundabout, they take 15 seconds to travel 50 m around the roundabout. If the roundabout has a radius of 20 m and assuming uniform circular motion.

a) What is the reading on their speedometer? [2 mark]

b) What is the angular velocity of the car? [3 marks]

**Question 4.**

A student decides to go on the L-park rotor ride. The ride works by the student standing towards the edge of the circle room. The room begins to rotate and the floor falls away once they reach a certain speed. If the diameter of the room is 30 m, it has a period of 10 seconds and the student weighs 60 kg, what is the force pinning them to the wall? [3 marks]

**Question 5.**

If a car is only designed to have a maximum centripetal acceleration of 50 m/s/s, what is the maximum speed it can go around a radius of 25 m [1 mark]

## Answers to Circular Motion HSC Questions

**Question 1.**

Angular velocity

**ω** = (2 * π)/ 3 rad/sec

- The same for both coins

(+ 1 mark for reaching this)

Tangential velocity

Inner coin

v = 2 π r/ t= (2*2*π)/ 3

Outer coin

v = 2 π r/ t= (2*8*π)/ 3

- Greater for the coin that is closer to the outer edge, hence most likely to fly off since it will experience the greater centripetal acceleration, meaning more friction will be required to oppose it.

(+ 2 marks for this conclusion)

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**References**