Chapter 16 Circular Motiom Flashcards
What is angular velocity
Just as velocity is displacement over time, angular velocity is angle travelled (in radians) over time
What is anglular velocity when talking about one revolution ,
Here the time would be the time period T (time taken for one revolution)
And the angle would be one revolution = 2 pi
So angular velocity would be 2Pi/ T
If we use frequency in angular velocity what does it become
Omega = 2PiF as 1/t = F
What are units for angular velocity
Rad per second
What does the frequency of rotation actually represent?
How many revolutions PER second
And time period is time taken for ONE REVOLUTIOM
So can interconnect
How else can you think about Angus,r velocity in terms of rotations
Rotations per second, greater angular velocity = greater rotations per second
What is uniform circular motion
What assumption allows us to use equations
For a body ti be rotating at a CONSTANT SPEED
If not constant speed then not uniform, yh the direction is changing all the time tho
So what is Angular velocity again and relate to LINEAR (OR CENTRIPETAL )velocity
Linear velocity is the displacement /t = 2PiR /T
Thus relationship between linear velocity and angular is V = wR
What is the only condition for circular motion to happen
What type of force is this known as?
That there is a constant force PERPENDICULAR to the velocity of the object at all times
- towards the centre
This is known a CENTRIPETAL FORCE
Why does a centripetal force cause it to have a constant speed but change direction
1) force explanation newton 2nd law
Force is directed inwards, so the acceleration inwards too
- as there is no component of the resultant force in the direction of the tangential velocity, it does not affect its speed,
- however in order to accelerate still it needs to change velocity, and if speed is constant, then direction must change
Thus direction changes
Why does direction change but not speed with centripetal force (perpendicular) ENERGY EXPLANATION
as there is no work done by centripetal force due to it being angle 90 cos 90 0, it remains same mechanical energy before, so kinetic energy dint change and speed does
But in order to accelerate inwards in direction if force, must change direction
The fact that linear V = wR, what does this tell you about a linear velocity and radius
Proportional to radius if angular velocity is kept the same , double radius fir same angular = double linear velocity
What is the formula for centripetal acceleration and where does this act
Thus using omega how ?
This acts directly to the centre and is v2/r
Thus a = w ^2r
How can we determine an equation for centripetal force
As centripetal, force acting perpendicularly ti velocity is CONSTANT, we get constant a so can use f =ma
F = ma
A = v2 /r
F=mv2/r
How else can centripetal force be written using angular velocity
F = m(w)2/r
=f=mw2r
As v= wr
Where f is always towards the centre if circular path
What forms can centripetal force be?
This can be
- frictional force provided when car turns towards the centre of the roundabout
- weight of a satellite provided by gravtwitonak field towards centre of mass
- tension in pendulum moving
- elec fields too, anything with circular motion
Explain how not slowing down when turning causes you to “spin out “ in a car
The centripetal force provided when turning is from the FRICTION of the car. However at a certain point this is at a maximum based on coefficient of friction, so you now have a constant
For this Fmax = mv2/r
For your certain mass , if your velocity is too high, then the radius will INCREASE to meet the maximum frictional force
If the velocity is too low then RADIUS will DECREASE too meet the maximum frictional force
Thus if you don’t slow down then the radius will increase, and you get the illusion of SPinning out when inf act your are jus increasing radius of circular motion to meet centripetal force required to perform it. But since you can’t increased radius whole system collapses
If that’s the case why do we use BANKED SURFACES to increase max velocity when turning
Banked surfaces means that not only is a component frictional force contributing to centripetal but also a component of the NORMAL force
Thus more force is contributing , so a higher velocity can be used to achieve circular motion for a grieved radius before it must increase, ie can travel faster on same turn now
The questions normally give you as the banked surface as smooth. What to do here and what is going on (what contributes to the centripetal force)
How to find max velocity
Smooth surface = no friction (or if it says coefficnt doesn’t apply)
As a result the only thing contributing to centripetal force is the component of normal force in horizontal = nsinx
As a result can make equations for N the normal and equate
N Sinx = mv2/r
And ncosx = mg
If you divide them now you get tanx relationship which you can rearrange for max safe velocity here!
In banked surfaces problem where is the centre? What direction
Same as spinning a bucket, it’s a t the centre horizontally, so need hroixntsl friction if using snd horsintak normal
Centripetal force = mv2 /r, but what can actually contribute to this
This firce can be made up of the normal, weight both jus friction, gravitational force etc
So if n rollercoaster at three points what is the normal l
They must all add to mv2/r
So 1) when at ground
N-W = F, so N = W+F
2) at side
N only firce in direction of centre , so N =F
3) at top
-N-W=-F, so N= F-W!
Jeee you can see how they add up to make the centripetal force
Okay so what’s centrifugal force? Is it real? What is the firce that you feel “pushing you out” on a turn
No such thing as centrifugal force, fake force that you “feel” on a turn as pushing you out, instead it’s your resistance to acceleration as you continue in that direction until the car pushes you
It’d the REACTION force from the car as it accelerated centriptsllg
You were asking why does the one plane have ti be resultant 0
‘This is because if there is no acceleration in this plane , then it will, be zero so they cancel out
Why do we experience a centripetal force
And why only at equator
As the Earth rotates we rotate too, and thus there is centreprta, force as our velocity remains CONSTSNT
This acrs at equator because earth spins on an axis
What does having centripetal acceleration mean for our normal at the equator vs poles
The fact that we have Cenriperal force means there is a RESULTSNT FORCE acting towards the Earth = mv2/r
This MUST be provided by weight and normal. As there is a resultsnt, the weight must be BIGGER THAN NORMAL, so normal is LESS
Therefore at equator less normal = LESS reading on scale
Whereas at poles no acceleration, so weight = normal as resuktsnt force is 0
How to calculate the centripetal accerlwtion experienced by everyone
A = v2/r
= w2r
2 = 2Pi/T
Where t is the time taken for one revolution
= one day
At banked surfaces, why is normal not equal to MGcos theta like normally ?
Because it acc procided for centreptal force AND balancing the weight
So the normal is actually greater
So you need to use Nein theta and N cos theta to make a tan relationship to find max safe velocity
Normal chnsges on London eye but why do you feel different heavy as it goes
Because feeling of weight determined by normal
So when this goes less , Ed
Socially at the top, then yiu can feel weightless
Similar concept for banked surface as a pendulum swinging a weight hiroxntslly?
What will the force from tneiosn must = to (two)
What equations made
The weight in y direction
And the centripetal force in x direction
AKWYAS MAKE SURE WHERE ACCLERSTION IS 0 FORCE IS THERE TO COUNTER
So T cos theta = mg, t sin theta = mv2/r
