Chapter 16 CIRCULAR MOTION

Question 1

What is the definition for radians

How ti get to 360° = 2Pi radians

Answer 1

1 radian is the angle subtended when the arc length is = to the radius

Therefore EQUATUIN is angle = arc length / radius

Since one full revolution arc lentgh = 2PiR

Angle in radians in 360 = 2PIR/R = 2Pi

So 2 Pi rad in 360°

Question 2

Why do we opt for angular velocity instead of linear velocity for all points in a circular motion

Answer 2

Because things closer ti centre will travel less distance in same time compared to things at edge of circle, so their VElocities are different

HOWEVER, all points travel through thr same angle in the same period of time

Thus their ANGULAR VELOCITY IS THR SAME AT ALL POINTS

Question 3

Angular velocity

Answer 3

= angle moved I’m radians / time taken

But if it’s not full revolution, then the time taken is = to the time period

So angular velocity would be 2PI/T

Question 4

Convert angular v equation ti frequency

Answer 4

As f = 1/T, it becomes 2PIF

Question 5

What does frequency of rotation mean

Answer 5

This means the number of revolutions per second

1/T

Question 6

What is uniform circular motion

Answer 6

A body’s rotations at CONSTANT SPEED

If it wasn’t constant then it wouldn’t be unfikrm

Question 7

Why when a body is experiencing circular motion it is experiencing accelrwtion

Answer 7

As it changed its direction, it’s velocity changes at all times, thus it’s acclerwitng

Even tho its keeping its speed

Question 8

What is the ONLY way a body can keep its same speed whilst changing direction and thus acclerwign

Answer 8

Accelrwtion, means there has to be a RESULTSNT FORCE

However if this resultsnt firce is in the plane of the velocity vector, then work WILL BE DONE in that plane and it will increase speed

The only way to ensure velocity stays the same is if the resultsnt firce is perpendicular to the velocity vector , AT ALL TIMES

this will thus change the direction , whilst keeping the speed constant

If the force is ALWAYS PERPENDICULAR to the velocity vector, then the body will experience uniform circular motion, with a centripetal sccelrwtion acting towards the centre caused due to a centripetal force acting towards the centre

Question 9

Condition for circular motion

Answer 9

Firce consntslyt acting perpendicular to velocity vector
- acting TOWARDS THE CENTRE OF ROTATION

Question 10

What it the linear velocity of a point in a circular motion

Relate angular velocity ti linear velocity

Answer 10

This is the TANGENT velocity vector acting at the radius

This is the speed that thing is moving at

Here v = distance / time
So 2PiR /T

Thus v = w r

Question 11

So for points on a circle they all have the same NAHULAR velocity, which Ken’s will have greater linear velocity

Answer 11

Greatest linear velocity is greatest radius away

Question 12

Equation for centripetal acceleration

I’m omega terms?

Answer 12

Linear velocity sqaured / r

Sun in v = wr

Will get a = w2 r

Question 13

Why do we EXPERIENCE A centripetal force at the equator of earth

Why not poles

And why in the first place

Answer 13

Only at equator because the earth rotates about a central axis to

Question 14

When turning on a roundabout, why when you dint slow down do you spin out?

What’s going on

Answer 14

Basically for you to spin in circle , there has ti be a centripetal force acting towards the centre

This comes from the FRICTION between tires and car

• this value can take a max value. As a result , the mv2/r is maxed at a constsnt
• if you going too fast, the RAIDUS of the motion will INCREASE so that the ratio matches the friction
• if you increased radius of turn, then yiu can travel FASTER too

So yeah it’s bounded

Question 15

What provided centripetal force

Answer 15

Can be weight, normals, tension, friction anything, gravitational attraction in the case of earth rotating around the sun

Or a satellite

Question 16

Why do we use banked surfaces then ti achieve higher speeds!

Answer 16

On a normal surfsce max Cf is capped due ti friction

In a BANKED SURFACE, not only is the Cf provided by friction component but ALSO a component of the NORMAL force

Thus for a given radius, if the centripetal force max has increased for the same mass, the velocities achieved can be greater too

Question 17

WHAT TO REMEMBER ABOUT NORMAL FORCE ON A BANKED SURFSCE

WHY IS THIS NOT = TO THE VERTICAL COMPONENT OF WEIGHT

2) so if it’s a smooth surface how can you find the max safe velocity using normal equations

Answer 17

Remember the normal balances the weight AND provides centripetal force

Thus the normal IS NOT equal to the vertical of weight

So you have new equations
N sin theta = mv2/r
N cos theta = mg

Can divide to make tan relationship and find max safe velocity

Question 18

Why are normals different around London eye,
At bottom
At top
At side

Remember how ti find it

Answer 18

Direct the force to the centre
Make it so there is an overall force in thst direction

And then see how NORMAL CHANGES

So at bottom, normal bigger than weight

At top weight bigger then normal = fc

At side only normal provides = fc

Question 19

Thus on a London eye do you feel different weights?

What causes feeling of weight

Answer 19

Yes because feeling of weight is the normal

So when normal goes less and higher yiu feel (weightless etc) at times

Question 20

What is centrifugal force finally pushing you out when you turn a car

Is it real?

Answer 20

No it’s the REISTANCE to you accelerating in the direction of turn as you continue in the velocity you were already at

This is caused by the walls or seatbelt etc

You continue at your velocity until you are pushed by centripetal force from car or whatever

Yh just centripetal force pushing you in accelerating you

Question 21

Is there an equal and opposite force?

Answer 21

There is

Question 22

Another word for linear velocity

Thus if centripetal force were to cut, what direction would it move in

Answer 22

Tangential

2) would. I’ve tangents, ti circular path at that time