Unit 3.1 - Circular Motion Flashcards
Definition of period in waves
Time for one complete cycle
Definition of frequency in waves
The number of cycles per second
When referring to circular motion, what is the same as saying “one complete cycle” in waves?
1 full rotation
Unit for period of rotation
s
Period of rotation (s)
The time it takes an object to complete 1 full circle
Frequency unit
Hz or s-1
Frequency (in terms of circular motion)
The number of rotations the object undertakes per second
What are radians?
Units for an angle
Definition of a radian
The angle at the centre of a circle where the arc is equal to the radius of the circle
What is 1 radian equal to?
About 57.3 degrees
Radian unit
rad
Why do we use radians as opposed to degrees?
Easier maths
Radians in 1 full circle
2π rad
Circumference of a circle
2πr
Half a circle in radians
π rad
Quarter of a circle in radians
π
— rad
2
180 degrees in radians
π rad
Converting from radians to degrees
Just remember that π = 180 degrees, and input this into the equation
Degrees to radians equation
Angle in degrees
———————— x2π
360
What do we leave radian calculations in terms of?
π
What is angular velocity also known as?
Angular frequency
What does our measurement the radian helps measure?
Th angle subtended (drawn out) by an object moving in a circle
Angular velocity/frequency symbol
ω
ω
Angular velocity/frequency
Angular velocity
The rate of change of angle measured in radians per second
Angular velocity equation
ω = angle
———
t
How is the angular velocity equation altered for a full rotation of time period T?
ω= 2pi
——
T
Which radian measurement is used for a whole circle?
2 pi
Equation for relationship between period and frequency
T = 1/f
Angular velocity equation involving frequency
ω = 2pif
Explain in detail what centripetal force is
Newton’s first law states than an object stays still or keeps moving in the same direction with the same speed unless a force acts upon it
If an object is moving in a circle, its direction is changing (even if it’s moving at a constant speed)
Since the direction is changing, there must e a force acting on it
F = ma (Newton’s second law), therefore the object must be accelerating
The forces that are acting on the thing that’s moving are known as centripetal forces
When whirling a hammer in a circle, describe its velocity
Will have a velocity at a tangent to the circle
What happens to the velocity of a hammer if its whirled at a constant rate?
The magnitude of the velocity won’t change, but the direction is constantly changing
How come a hammer being whirled around is accelerated due to the centripetal forces?
The direction of the velocity is constantly changing, so the velocity is changing, so the hammer is accelerating due to a force
What is the force provided by in a hammer being swung around and what does this mean?
Provided by the chain
So, force acts in the same direction
What is constant and what isn’t in centripetal acceleration (when spinning at a constant rate)?
Magnitude = constant
Path = not constant
What is constant when something is spinning at a constant rate, even though the object is accelerating in a certain direction? Which direction is this?
Speed = constant
It accelerates towards the centre of the circle
Centripetal force
Causes centripetal acceleration, which is always directed towards the centre of a circular path
What does a centripetal force keep an object doing?
Moving in a circle
What would happen to a spinning object once the centripetal force is gone?
It would accelerate in a straight line
Is centripetal force a type of force?
No
If centripetal force isn’t a type of force, what is it?
It’s the name given to a force that causes an object to move n a circle - the force is provided by a type of force
Force that provides the centripetal force during the orbit of the earth around the sun
Gravitational
Force that provides the centripetal force during a car cornering
Frictional
Force that provides the centripetal force with a child on a swing
Tensional
Force that provides the centripetal force with a child on a roundabout
Frictional
Force that provides the centripetal force during an electron orbiting a nucleus
Electromagnetic
Force that provides the centripetal force on a wind turbine
Tension
Forces that provide the centripetal force during a car turning on a banked track
Component of normal reaction and friction (less friction than on a flat road due to the normal reaction force being there too)
What is proof that force is directed towards the centre of a circle?
If we take the vectors of two velocities on a circle, their change in velocity is directed towards the centre of the circle
Linear velocity on a circle equation to learn
v = 2pir/T
(2pir = circumference of a circle)
(T = time period for a full circle)
What does a higher radius result in for an object with circular motion? Provided what?
A faster velocity
Provided that ω is constant
Why does a higher radius result in a faster velocity for an object with circular motion?
More force is needed to keep it moving in a circle
What happens to the acceleration of an object with circular motion when it has a higher radius and why?
Higher radius = faster velocity as more force is needed to keep it moving in a circle
Therefore, more acceleration is needed to keep it moving in a circle
Equation relating angular and linear velocity
v = ωr
Equation relating centripetal acceleration and angular velocity
a = ω^2r
Centripetal acceleration
Acceleration needed to keep an object moving in a circle
Acceleration needed to keep an object moving in a circle
Centripetal acceleration
Derive a = v^2/r
Rearrange v = ωr to ω = v/r and place it into a = ω^2r
a = v^2/r
Difference between v and ω
v = linear velocity
ω = angular velocity
How do we derive the two equations for centripetal force?
Use the two expressions for acceleration in Newton’s second law equation (F = ma)
So, use a = ω^2r and a = v^2/r in F = ma to get
F = mω^2r
and
F = mv^2/r
In which direction is the acceleration of circular motion?
Towards the centre of circular motion
Discuss how their application of science enables cars to travel safely around curves
Appropriate surface
Appropriate tyre design for friction
Banking of road for contribution of normal contact force
Suspension set up
What are the 2 equations for linear velocity to learn?
V = 2pir/T
And since f=1/T,
V = 2pirf
Which forces make up the centripetal force in vertical circles?
Tension in the string
Weight of the object
Equation for centripetal force at the top of a vertical circle
Centripetal force = weight + tension
Equation for tension at the top of a vertical circle
Tension = centripetal force - weight
What is constant on all points of a vertical circle and why?
Centripetal force
v is constant
What needs to be higher at the bottom of a vertical circle and why?
Tension force in the string as weight acts in the opposite direction to centripetal force, and the centripetal force is constant
Equation for centripetal force at the bottom of a vertical circle
Centripetal force = tension - weight
Equation for tension at the bottom of a vertical circle
Tension = centripetal force + weight
Where is there a higher tension on a vertical circle and why?
At the bottom
As tension needs to be higher to keep the centripetal force constant as weight now acts in the opposite direction
Why does it feel like there’s more force at the bottom when spinning something around?
As there’s higher tension at the bottom
What is revs.min-1?
A form of frequency
What value do we use if something is “weightless” in a question?
a = 9.81ms-2
What value do we use if something is at “minimum speed” in a question?
a = 9.81ms-2
What value do we use if a question is asking for the “acceleration needed to just remain taut throughout the motion when rotating in a vertical circle”?
a = 9.81ms-2
Degrees to radians
Degrees x 2pi/360
Radians to degrees
Radians x 360/2pi
Why is a car accelerating when moving in a circle?
Direction changing = velocity changing = accelerating
