3.1-3.2 Circular Motion

Let’s take a look at your diagram

During your investigation, you might have noticed a few things when you released the stopper at various points

Is velocity constant when an object moves in a circle?

Can you keep an object moving at a constant velocity when it moves in a circle?

THE ANSWER IS YES AND NO What aspect of velocity can you keep

constant? What aspect of velocity changes?

Direction changes, speed is constant

Even though only one aspect of the velocity vector changes, that still means change

And a change in velocity means… ACCELERATION And where there is acceleration, there

is… FORCE

Constant speed, changing direction

Circular motion can be seen as a large number of straight velocity vectors adding up to give you circular motion

Much like a circle itself can be made up of a large number of small straight lines

The smaller those lines are, the closer you get to a perfect circle

See the progression?

What forces do you feel?

When you are spinning the mass, what forces did you feel?

What keeps the mass from flying out of the circle (which is what happens when you let go…)

Centrifugal vs. Centripetal force

You will notice that when the mass spins, it pulls out of the circle

Think about what happens when you spin a small child around by their arms – what do you notice?

This force – the force that a spinning mass seems to exert outwards – is known as the CENTRIFUGAL FORCE

What keeps the mass from flying away?

If the mass pulls outwards during circular motion, the one thing keeping it from flying out MUST be an opposing force inwards

In the case of your little experiment, what was it?

Centripetal force

In the case of your experiment, the tension in the string provides what is known as a CENTRIPETAL FORCE that pulls inward

This constant force “yanks” the mass inwards, forcing the velocity vector to constantly turn inwards

Therefore, if the force pulls inwards – so does the acceleration it causes

Centripetal force is external to the mass

This could be string, a rod – anything that is attached to the rotating mass that keeps it from flying out of its rotational circle

Even gravity – planets move around the sun at a constant speed in a circular motion because the sun’s gravitational pull creates a centripetal force that keeps us in orbit

If the planets did not maintain a constant speed, what would we notice on earth?

Which one do we pay attention to?

Essentially, if an object is moving uniformly in a circle, it means that the centrifugal and centripetal forces are balanced out

Most questions will ask you to find centripetal force – and usually it is assumed if we are dealing with uniform motion that they are equal

Centrifugal force is described via the the rotating mass

Centrifugal force is a necessary “invisible” force used to describe the path of objects moving in a circle

Since a rotating object is in a non-inertial frame of reference that means that the forces the mass experiences must be explained somehow

As you spun the mass faster, what did you notice? The greater the speed of the object rotating, the larger

the centrifugal force, therefore requiring a larger centripetal force to keep it in a circle

A false force

Centrifugal force is a false force – it is the force “felt” by an object due to its inertia

The object wants to maintain its motion, so it resists the centripetal force being applied

This gives the impression of a “force” being produced that opposes the centripetal

Fcp

v1

v2

Centripetal acceleration pulls inwards – but don’t forget that the mass “pulls” outwards creating the sensation of centrifugal acceleration

Fcf

Fcp

v1

Fcf

At an instant in the object’s path – notice that the vector doesn’t change in its position either inwards or outwards – rather, if released, will move tangentially away – thus Fcp and Fcf are balanced

The equations

So how do we get the numbers? The equation for centripetal acceleration

is determined by looking at the velocity vectors at an instant and another measureable quantity in the motion of the circle – the radius