Circular Motion Chapter 16 Flashcards
Angular velocity
Is the angle in radians covered in time
When time = T, then the angle covered must be 2Pi, hence 2Pi/ T
This is given symbol omega
As 1/T = f, it can also be 2Pif
If they give you the frequency of rotation, revolutions per second, how to find Angular veoclotu
Remember 2Pi x f, may spin 7 times per second, so this means the angle covered is 14Pi per second
Linear / tangential velocity
= omega r, that’s why the anhualr velocity is the same everywhere on the circle, but the tangential velocity deoends on the radius, as things further away is moving faster than closer
What is circular motion and how is it achcibed
Why is the direction only changed?
It is when a CONSTSNT perpendicualr force is applied cosntnskty to the velocity vector, aimed towards the CENTRE OF ROTATION
- as there is no component of force applied in the same direction as velocity vector, work is not done in that direction, hence the speed stays the same, but the direction changed
What is the cnetipretka FIRCE and accerlwtion
Centripetal force is the force that causes centripetal accerlwtion, all circuslr motion bodies experience this, anything that’s rotation
The force is aimed at centre of rotation and is = to MV2 /R
ANYTHING rotating , (even us on earth ) Will experience a centripetal force as we are accelerating in that direction
- if we experience a centripetal force , then there must be a resultant force that PROVIDES IT
therefore what can contribute to centripetal force
Tension from a string, normal force from ground, friction when driving , gravational force from planets too
Oh also elec fields, mass spec mag fields experience ciecuskr motion too
Anythign, as long as there is a resuktsnt force in that direction it will cause centripetal accerlwtion provided this force is perpendicualr to the twngents, velocity
Explain car spinning out situation
There is a maximum friction force that can be applied during turning, and therefore a ratio set up
, base don thr mass, if the car is moving toknfast on the turn, the rwofus will increase to make it equal to the cnetipetwl force, and so spins out. Thus there is a MAX safe speed of turning for a given mass , based on the radius of turn…
So how are BANKED SURFACES used, to increase the velocity of safe speed?
However how are normal banked surfaces qs like
As well as the friction contributing to the centripetal force, now so is the NORMAL as it’s not perpendicualr to the direction of rotation
MUST REMEMBER, whenever there is acceleration (centripetal or normal) the NORMAL FORCE IS NEVER THE SAME AS WEIGHT . Resolve vertically and you’ll see
The centripetal is always RESULTANT
2) normally they say the surfsce is smooth, therefore friction is not there, so tie lit just the normal force providing centripetal force for accerlwtion
To find the max safe velocity now, find the centripetal force using equations and then use mv2 /r to find answer
Remember the centre is ALWAYS CENTRE OF ROTATION , look how he’s rotating and see
How to find the cnetirpetal scclerwtion if someone standing around the earth
Remember, as earth spinning, we all edepriwmce centripetal acceleration
EXCEPT ON THE NORTH AND SOUTH POLE, WHERE THERE IS NO ROTATION
- can calculate using omega equation and time period of 24 hours
- now as we accelerating, what gives us FIRCE in that direction, MUST BE THE WEIGHT , therefore anywhere but poles on earth, some compoenent of weight is resuktsnt to give us the resuktsnt force, and thus WEIGHT is greater than normal
A weighing scale can only detect normal force. On the poles of the earth, no acceleration so normal = weight. As a result normal force is maximum on the poles and minimum at equator, therefor, weighing scale reads max on poles, and we also “feel “ heaviest because we only feel our weight as the result of the normal force exerted
As you go around the earth the normal increases as the weight force is only a component?
Rollercoaster example
At the top the weight provides centripetal, the weight has ti be greater than normal
At the bottom. Or al had to be greater than weight
At the side remember normal = centripetal force
These all change how much you feel when normal is 0 , perhaps at the top, when velocity so fadt, normal can be 0
Rememebr what’s the lowest normal can be for you to still be in contact with the rollercoaster
Normal has to be 0, as soon as it becomes negative you fly off
As pendulum swings a weight horinxtally what’s going on
Here thr tension accounts for both the weight of the corker and the centripetal force acting towards the direction of centre
However at really fast speeds , t sin theta value will be SXTREMELY large due to mv2/r, comapred to MgO which is t cos theta , it’s barely nothing
So at very lasergeschnittenen speeds , tension is roughly the same as the centripetal force, and this happens at large speeds, and thus at SMALL ANGLES, because the faster it goes, the smaller the angle is
When making equations equal how to don
Why is it impossible for the rope to swing horizontally completely
Always see which plane there should be 0 acceleration, and then set that to 0
Therefore it is impossible for the rope to swing horizontally , as there won’t be a component to oppose the weight
