Chapter 16 CIRCULAR MOTION Flashcards
What is the definition for radians
How ti get to 360° = 2Pi radians
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°
Why do we opt for angular velocity instead of linear velocity for all points in a circular motion
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
Angular velocity
= 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
Convert angular v equation ti frequency
As f = 1/T, it becomes 2PIF
What does frequency of rotation mean
This means the number of revolutions per second
1/T
What is uniform circular motion
A body’s rotations at CONSTANT SPEED
If it wasn’t constant then it wouldn’t be unfikrm
Why when a body is experiencing circular motion it is experiencing accelrwtion
As it changed its direction, it’s velocity changes at all times, thus it’s acclerwitng
Even tho its keeping its speed
What is the ONLY way a body can keep its same speed whilst changing direction and thus acclerwign
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
Condition for circular motion
Firce consntslyt acting perpendicular to velocity vector
- acting TOWARDS THE CENTRE OF ROTATION
What it the linear velocity of a point in a circular motion
Relate angular velocity ti linear velocity
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
So for points on a circle they all have the same NAHULAR velocity, which Ken’s will have greater linear velocity
Greatest linear velocity is greatest radius away
Equation for centripetal acceleration
I’m omega terms?
Linear velocity sqaured / r
Sun in v = wr
Will get a = w2 r
Why do we EXPERIENCE A centripetal force at the equator of earth
Why not poles
And why in the first place
Only at equator because the earth rotates about a central axis to
When turning on a roundabout, why when you dint slow down do you spin out?
What’s going on
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
What provided centripetal force
Can be weight, normals, tension, friction anything, gravitational attraction in the case of earth rotating around the sun
Or a satellite
Why do we use banked surfaces then ti achieve higher speeds!
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
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
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
Why are normals different around London eye,
At bottom
At top
At side
Remember how ti find it
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
Thus on a London eye do you feel different weights?
What causes feeling of weight
Yes because feeling of weight is the normal
So when normal goes less and higher yiu feel (weightless etc) at times
What is centrifugal force finally pushing you out when you turn a car
Is it real?
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
Is there an equal and opposite force?
There is
Another word for linear velocity
Thus if centripetal force were to cut, what direction would it move in
Tangential
2) would. I’ve tangents, ti circular path at that time
