## Twistin’ and Turnin’ – Circular motion will set your brain a-burnin!

So. You’re back – you survived one year of physics, and you decided to come back for another. If you’re smart, you’re a bit scared! If you’re smarter, you’re already working your backside off and planning how you can work harder. This year we are starting with a review of 1-D kinematics from last year, and quickly moving into 2-D applications of the same ideas. The first one we are spending time on is circular motion – that is objects moving in a circle in either the vertical or horizontal plane.

Circular motion is hard to get your head around in the beginning, because your own experience is lying to you. Everyone has ridden in a car as it goes around a corner in the road or a roundabout – and you have felt the force “pushing you towards the outside of the curve”, so when you think about these forces, you have an immediate expectation that the force is acting outwards – from the centre of the circle out…

But you would be wrong!

A simple thought experiment (now there’s a phrase you will grow to hate this year!) quickly shows how the direction of the force must
be inwards (not outwards as your initial impression may be). Two parts to this mental excursion – firstly it is easy to see that you cannot push with a string – you can only pull. Secondly, if you attach a string to a pendulum and swing it around so it travels in a circle, you can quickly see that the only reason it travels in a circle is that the string pull it inwards – that means that the force on the pendulum must be towards the centre – not outwards, but inwards!

This is the first weird thing about circular motion – that the force is towards the centre. This is apparent in the name of the force – the centripetal force. The word itself tells you that the force acts inwards – the “pet” in centripetal is the same etymology (word origin) as appetite – and when you are hungry (you have an appetite) you put food in your mouth, and in the same way, a centripetal force acts inwards.

You have read and summarised the textbook sections on circular motion, but here are some additional Circular motion notes. There is a section in the textbook that attempts to give the derivation of the formula for centripetal acceleration, but even for someone who already knows it, it isn’t very clear. While you will never be asked at this level to give the derivation, understanding how it is calculated will give you an advantage over students who have not invested that effort. To that end, I strongly suggest that you view this YouTube video. It does a good job of explaining the origin of that critical equation. Note that the video uses the lower case delta (δ) instead of the upper case delta (Δ) that we usually use in Australia.

Just like the guy in the picture to the left, you need to ride physics like a boss – don’t get strapped down and do your physics like a passenger – stand up and rule it like a king!

To that end, you want to look at the following three (1, 2, 3) powerpoints that explain some of the critical concepts and shows some calculations that are typical assessment type questions. Last of all, you may want to watch the following – but not if you are feeling nauseated or are scared of heights or carnival ridges (direct link if necessary). Try and keep your physics brains on during the show – it makes it all the more terrifying.

Finally, I want each of you to put a comment on this post giving an example of circular motion that you have either found online or experienced yourself, and discuss how the physics you have learnt applies to that situation. This is a critical task and an essential skill – you must learn how to use the science of physics to explain phenomena in a concise and coherent way. The only way you are going to get good at this is practice – and I intend to help you get that practice.

Explore posts in the same categories: Kinematics, Physics, Year 12

### 24 Comments on “Twistin’ and Turnin’ – Circular motion will set your brain a-burnin!”

1. Prathu Khairnar Says:

Woah this is so much help! i am looking forward to stalk your posts this year 😀

Prathu

• CyberChalky Says:

Hi Prathu,
You don’t get away that easy! You are most welcome on this blog to join my little community of learners/victims, but I’d appreciate your full participation. So where’s your comment on your observation or experience of centripetal forces?

• Prathu Khairnar Says:

There once was time when Prathu went to luna park. Prathu was “forced” to sit in those horizontal “Ferris wheel”… please excuse me, i tend to have forgotten what they are called. Prathu observed nice chairs, encased and disguised as animals – such as ducks, dogs, and a bee. as soon as Prathu sat in one of those, and as soon as they started moving.. Prathu saw colours and stars, and fainted (true story).

calm down, i was just trying to be funny. so anyways, i experienced, rapid acceleration at the start, and then constant changing of direction. although the cart i was sitting in was being pulled towards the center, as u mentioned before. i felt like i was pushed outside the cart. now that i think of it, i think it was probably because i was heavier back then.

woah thats interesting, would the force pushing u outside the cart increase if your mass increase? — > i think yes, because the more mass i have, the greater inertia i would have. the fact is that, the cart is physically attached to the center of the “horizontal ferris wheel”. the cart is constantly changing its velocity (only the direction) – and thus also changing acceleration (only the direction).

but the point is, if the cart was being pulled inward, why was Prathu being thrown(pushed) outside the cart? …

i experienced greater force pushing me outside the cart, as the rotations per minute increased.

i really have stumbled now, because i am not 100 percent sure about the cause of this thingy, i think its inertia, but i might be wrong.. the thing is, i was moving at a speed but since the cart changed direction, it doesnt mean i have to change it too.. so maybe thats the reason why i was being forced outside.. hmmm…

• CyberChalky Says:

Hi Prathu,

Now you’re beginning to get into the confusion of centripetal forces/ circular motion. It is good to do this now, and not when you are revising later for and assessment task, or horror of horrors, the *massive* end of year exam. You are absolutely correct – there is a distinct sensation of an outward force, and you’re right to link it to inertia – better stated as Newton’s first law – but you also need to take into account the third law. Add to this the idea that change in direction of velocity requires a force just as much as change in magnitude of velocity, and you should be able to start working it out.

I am a little surprised at your choice of context (a horizontal Ferris wheel is called a carousel, or sometimes a merry-go-round). I was very much expecting it to have /something/ to do with architecture – a space station or similar…

2. Frances Rowlands Says:

Thank you for the notes they helped make the concepts much clearer.

Here is my example:

If you spin a yo-yo (on a string) in a circle, although the magnitude of its velocity may be constant, the direction of its velocity is constantly changing. What causes the yo-yo to go in a circle is your hand holding the string and providing tension into the string. The centripetal force in this example is the tension in the string that constantly pulls the yo-yo towards the centre of the circle.

• CyberChalky Says:

Hi Frances,

An interesting observation. Can you take it a little further? The yo-yo itself is rotating on the end of the string – does this have any effect on the behaviour of the yo-yo? Or perhaps you could discuss how the different masses of yo-yos alter the way they travel “round the world”?

• Frances Rowlands Says:

In my example I am assuming that the yo-yo is not spinning on the end of the string and that the string is completely unwound.

However if you wanted to spin a yo-yo of greater mass, but keep the speed constant you would increase the tension into the string or if you wanted to keep the same tension into the string you would have to decrease the magnitude of the velocity or increase the radius of the circle you are spinning the yo-yo in.

• CyberChalky Says:

Excellent consideration of the linked variables, Frances. You are right – it is easier to assume the yo-yo is not spinning, but if it did not spin in the real world, it wouldn’t work for many reasons.

3. Found the slideshows very helpful although I had left my physics workbook at school so I will be re-watching them to take down some of the helpful notes!

Here is my example of circular motion:
A electron stably orbits the nucleus of an atom.
The magnitude of the electron’s velocity is constant, however the direction of it’s velocity is constantly changing.
The force causing the circular motion is the attraction of the negatively-charged electrons to the positively-charged nucleus. The centripetal force in this example is the electromagnetic force, pulling the electron towards the centre of the circle (nucleus).

• CyberChalky Says:

An interesting example, Tessa. We will look more closely at electron orbits later this year. There are some very interesting physics associated with them…
Taking your scenario a bit further, what changes as the atomic number of the element gets larger, and what effects might this have on the forces acting on an orbiting electron?

4. Hayden Maughan Says:

Thanks for that Mr G, Helped get my head around it just that little bit more!

My Example:
In hammer throw the athlete gets to a point in which the hammers magnitude of velocity does not change but as he/she spins around the direction of the hammers velocity does indeed change.
The hammer on the end of the cord is being pulled towards the hands where the athlete is holding the grip. You can get an even better picture of the centripetal force in action on the hammer, for when the athlete lets go of the grip the hammer is projected at a tangent to the circle where is was being spun and no longer rotates around a circle.
???

• CyberChalky Says:

Hi Hayden,

A nice example – but let’s push it a little more away from the theoretical and into the practical. Given that the strength of the athlete does not change (i.e. the maximum force he is able to exert/tolerate is constant), which would of the following variables would be best to change – mass of the hammer or the length of the hammer strap? Can you relate your theoretical answer to the actual variety of hammers actually used in competition?

Ah… reality – the ultimate pain in the backside!

5. trentp95 Says:

Thanks Mr G i am starting to understand it i think but my example will make it clear to you if i don’t!

Alright my example of circular motion is the moons orbit around the Earth. The Earth exerts a pull on the moon, which keeps it orbiting the Earth. Since the Earth is larger in comparison to the moon, it pulls the moon towards the Earth moving at a constant velocity but as it goes around the Earth the direction is changing constantly providing acceleration. The centripetal force would be the earth pulling the moon and circling its orbit.
?

• CyberChalky Says:

Hi Trent,

Interesting exploration of the relationship between orbits and gravitational forces. Only problem I see is the sentence that says ” the direction is changing constantly providing acceleration” – I think you may have that backwards…

6. Locky Hampton Says:

Hey Mr. G , here is my example:

A racecar is racing around a bend on the track. As the car turns it is obviously accelerating, but not from the loss of speed, but from the change in direction. It turns the corner from the result of the inward directed net force applied form the wheels of the car, which is defined as a centripetal force. As you travel around any corner, you feel as if you are being thrown to one side of the car. This is the result of the car wanting to remain in motion in a straight line. It is the friction of the tyres ion the road that cause that produce the centipetal force needed for you to turn the corner. If you were to simply let go of the steering wheel midway through a turn, the inward force from friction will be lost and your car will seek to continue in motion tangent from the turning circle.

In this case the centripetal force that is exerted on you and the car would be the friction of the tyres on the road?

• CyberChalky Says:

Hi Locky,

You’re on the right track, but I think you need to unpack the second sentence a little bit. You say it is “obviously accelerating”. How is this obvious? Can you explain by resolving the sequential vectors? You are right to say it is the friction between the road and tyres that is the source of the centripetal force, and there is an easy way to tell. Just pour lots of oil on a sharp turn in a road and watch the passing traffic…

ps. Don’t do this. Really.

7. Matthew Tucker Says:

I watched that video and i was actually wondering if those rides were real… then i saw that big one that shot all the little cars in different directions and realized that it was fake….

My example of circular motion is – At an amusement park there is a ride that consists of a cylinder standing vertically with people lying against the walls of the cylinder. The cylinder then begins to spin and as it get faster and faster the floor drops away leaving the people stuck to the wall as it spins around. The wall is exerting a force on the people inside, making the people move into the circle, but their body is exerting an equal and opposite force on the wall so the result is that their body doesn’t move with respect to the
wall, and therefore, they stick to it.

it was a good read about Joe and Bobby. http://sciencecases.lib.buffalo.edu/cs/files/gravitron.pdf

8. Rowan Champion Says:

My example:
Objects or air being moved around in a tornado, the objects are kept in the tornado’s circular motion by the flow of the air

• CyberChalky Says:

A very interesting situation, Rowan. Because the shape of an ideal tornado is an inverted cone, what does that mean for objects trapped in the twister as they ascend?

9. Josh Sheldrick Says:

Hey Mr.G, thanks for the explanation 🙂
My Example for circular motion is two kids swinging with each other around in a circle, One will be standing on the ground and the other will have their legs up above the ground almost as if they are floating.

P.S Can you please leave an email address as I need to contact you about tomorrow work requirement.

• CyberChalky Says:

Hi Joshua,
Interesting example. What do you think happens if the relative masses change? For example, Can a smaller person swing a heavier person around? Why or why not?
Email me at 0816;41;79@mel?ba.v&ic.edu\$.-au (remove unnecessary punctuation marks).

10. Darcy Hamilton Says:

Hey, sorry i took so long to answer the post i didnt really understand it at first and then i just forgot to comment. The notes were helpful and made it clearer.

My example:
The rotor blades on a helicopter. If the blades were spinning at a constant speed, the magnitude of the velocity, of the tip of the blade, would be constant. However as velocity is a vector and the direction of velocity is constantly changing there would be an acceleration. The centripetal force would be the rotor pulling the blades inwards. If a blade were to detach it would fly off at a tangent to the point where it detached, also this would be a very bad situation for the helicopter pilot.

• CyberChalky Says:

Ok Darcy,
It’s good that you have your comment up. Take your example a step further- what (range of) length(s) are helicopter rotor blades? Why? How is this related to the centripetal forces?