Circular Motion Flashcards
Angular displacement
The angle through which an object moves in a given time
Measured in radians
Angular displacement formula
s=rθ
Angular displacement for a full circle
2π radians
Radians to degrees and vice versa
Shift
Set up
2
Linear velocity
Rate of change of linear displacement
Measured in meters/second
For an object in circular motion, its linear velocity is what
Tangential to the objects circular path
Constantly changing as the object moves around in a circle
Angular velocity equation
w=△θ/△t
Angular velocity
Rate of change of angular displacement
Measured in radians/second
rpm
Revs per minute
How many revolutions completed in a minute
rms(revs^-1)=Frequency=rpm/60
revs^-1 into rads^-1
x2π
Angular velocity given frequency
2πf
Angular velocity given time period
2π/T
Linear velocity given frequency
2πrf
Linear velocity given time period
2πr/T
Frequency
Number of complete revolutions per second
Is a ball swung around someone’s head accelerating if traveling at a constant speed in a circle
Yes
Speed is constant
But velocity is constantly changing since constantly changing direction
Acceleration = Change in velocity/time
What must act on a ball to keep it moving in a circular path when swung around a head
A resultant force
Centripetal force
Always acting towards the centre of rotation
Coming from the tension
What happens if the string swinging a ball in a circle snaps
No longer accelerates towards the centre
Continues moving at the same speed in the same direction as when the string snapped
Travels in a parabolic path in free fall from the side perspective (acceleration acting vertically down)
From above follows a tangential path, following Newton’s first law
Centripetal acceleration
Acts towards the centre of rotation and keeps objects in circular motion along with the centripetal force
What are the centripetal force and centripetal acceleration always perpendicular to
(linear) Velocity
What happens if the centripetal force increases
Either remains the same distance from the centre but at an increased velocity
Or moves closer to the centre and remains at the same velocity
What happens if the centripetal acceleration decreases
Either remains at the same distance from the centre but travels with a smaller velocity
Or moves further from the centre and continues with the same velocity
Centripetal acceleration for linear velocities
v^2/r
Centripetal acceleration for angular velocities
w^2r
Examples of centripetal forces
Gravitational attraction Friction Magnetic force Reaction and weight Tension Lift and weight
What forces contribute to the centripetal force
Any components of forces acting towards the centre of rotation
Centripetal force greater than maximum
Circular motion does not happen
Force is too weak to maintain circular motion
String breaks, car skids off roundabout
Centripetal less than or equal to maximum
Circular motion happens
What happens if a car enters a bend at a speed higher than the maximum speed
Centripetal force is greater than the maximum friction
Car will skid off and move to a greater radius
Circular motion couldn’t be maintained at that radius
Other phrases for reaction
Normal contact
Support force
What must be taken into account in vertical circular motion
Force acting readily (tension, reaction)
Weight (vertical component)
Increasing speed for non fixed radius
Centripetal force the same
Radius increases
Increasing speed for fixed radius
Centripetal force increases
Decreasing speed for non fixed radius
Centripetal force the same
Radius decreases
Decreasing speed for fixed radius
Centripetal force decreases
Centripetal force equation on the underside of the top of a loop in circular motion
Fcentri=W+R
Centripetal force equation on top of a loop in circular motion
Fcentri=W-R
Centripetal force equation on the bottom of a loop in circular motion
Fcentri=R-W
For a ball on a string in vertical circular motion where is tension maximum and why
Bottom
Fcentri=T-W
For Centripetal force to remain constant, the tension must be greatest here since weight is constant
For a ball on a string in vertical circular motion where is tension minimum and why
Top
Fcentri=T+W
For Centripetal force to remain constant, the tension must be smallest here since weight is constant
Does the highest speed a car can travel over the hill change for a car with greater mass
No
Stays the same since v max = root (gr)
g is constant and so is r so vmax stays the same
Mass is not included in the equation/vmax independant of mass
mv^2/r=mg
m will cancel because although two different masses being compared when working out the vmax its the mass of the same object
For a conical pendulum, what is the effect of increasing the velocity
Tension in the vertical direction must stay the same as it must be equal to the weight since in vertical equilibrium
Fcentri will increase since the tension in the horizontal direction will increase
So radius must increase
Meaning that the angle to the vertical will be greater
Why will a ball being swung in horizontal motion never be perfectly horizontal
The weight of the wall acts vertically down
In order for it to be in vertical equilibrium there must be a vertical component of tension of the centripetal force
Meaning that it will always be angled by some amount
