Chapter 16 Circular Motiom

Question 1

What is angular velocity

Answer 1

Just as velocity is displacement over time, angular velocity is angle travelled (in radians) over time

Question 2

What is anglular velocity when talking about one revolution ,

Answer 2

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

Question 3

If we use frequency in angular velocity what does it become

Answer 3

Omega = 2PiF as 1/t = F

Question 4

What are units for angular velocity

Answer 4

Rad per second

Question 5

What does the frequency of rotation actually represent?

Answer 5

How many revolutions PER second

And time period is time taken for ONE REVOLUTIOM

So can interconnect

Question 6

How else can you think about Angus,r velocity in terms of rotations

Answer 6

Rotations per second, greater angular velocity = greater rotations per second

Question 7

What is uniform circular motion
What assumption allows us to use equations

Answer 7

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

Question 8

So what is Angular velocity again and relate to LINEAR (OR CENTRIPETAL )velocity

Answer 8

Linear velocity is the displacement /t = 2PiR /T

Thus relationship between linear velocity and angular is V = wR

Question 9

What is the only condition for circular motion to happen

What type of force is this known as?

Answer 9

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

Question 10

Why does a centripetal force cause it to have a constant speed but change direction
1) force explanation newton 2nd law

Answer 10

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

Question 11

Why does direction change but not speed with centripetal force (perpendicular) ENERGY EXPLANATION

Answer 11

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

Question 12

The fact that linear V = wR, what does this tell you about a linear velocity and radius

Answer 12

Proportional to radius if angular velocity is kept the same , double radius fir same angular = double linear velocity

Question 13

What is the formula for centripetal acceleration and where does this act

Thus using omega how ?

Answer 13

This acts directly to the centre and is v2/r

Thus a = w ^2r

Question 14

How can we determine an equation for centripetal force

Answer 14

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

Question 15

How else can centripetal force be written using angular velocity

Answer 15

F = m(w)2/r
=f=mw2r
As v= wr

Where f is always towards the centre if circular path

Question 16

What forms can centripetal force be?

Answer 16

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

Question 17

Explain how not slowing down when turning causes you to “spin out “ in a car

Answer 17

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

Question 18

If that’s the case why do we use BANKED SURFACES to increase max velocity when turning

Answer 18

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

Question 19

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

Answer 19

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!

Question 20

In banked surfaces problem where is the centre? What direction

Answer 20

Same as spinning a bucket, it’s a t the centre horizontally, so need hroixntsl friction if using snd horsintak normal

Question 21

Centripetal force = mv2 /r, but what can actually contribute to this

Answer 21

This firce can be made up of the normal, weight both jus friction, gravitational force etc

Question 22

So if n rollercoaster at three points what is the normal l

Answer 22

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

Question 23

Okay so what’s centrifugal force? Is it real? What is the firce that you feel “pushing you out” on a turn

Answer 23

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

Question 24

You were asking why does the one plane have ti be resultant 0

Answer 24

‘This is because if there is no acceleration in this plane , then it will, be zero so they cancel out

Question 25

Why do we experience a centripetal force

And why only at equator

Answer 25

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

Question 26

What does having centripetal acceleration mean for our normal at the equator vs poles

Answer 26

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

Question 27

How to calculate the centripetal accerlwtion experienced by everyone

Answer 27

A = v2/r
= w2r

2 = 2Pi/T

Where t is the time taken for one revolution

= one day

Question 28

At banked surfaces, why is normal not equal to MGcos theta like normally ?

Answer 28

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

Question 29

Normal chnsges on London eye but why do you feel different heavy as it goes

Answer 29

Because feeling of weight determined by normal

So when this goes less , Ed
Socially at the top, then yiu can feel weightless

Question 30

Similar concept for banked surface as a pendulum swinging a weight hiroxntslly?

What will the force from tneiosn must = to (two)

What equations made

Answer 30

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