Unit 3.1 - Circular Motion Flashcards
1
Q
Definition of period in waves
A
Time for one complete cycle
2
Q
Definition of frequency in waves
A
The number of cycles per second
3
Q
When referring to circular motion, what is the same as saying “one complete cycle” in waves?
A
1 full rotation
4
Q
Unit for period of rotation
A
s
5
Q
Period of rotation (s)
A
The time it takes an object to complete 1 full circle
6
Q
Frequency unit
A
Hz or s-1
7
Q
Frequency (in terms of circular motion)
A
The number of rotations the object undertakes per second
8
Q
What are radians?
A
Units for an angle
9
Q
Definition of a radian
A
The angle at the centre of a circle where the arc is equal to the radius of the circle
10
Q
What is 1 radian equal to?
A
About 57.3 degrees
11
Q
Radian unit
A
rad
12
Q
Why do we use radians as opposed to degrees?
A
Easier maths
13
Q
Radians in 1 full circle
A
2π rad
14
Q
Circumference of a circle
A
2πr
15
Q
Half a circle in radians
A
π rad
16
Q
Quarter of a circle in radians
A
π
— rad
2
17
Q
180 degrees in radians
A
π rad
18
Q
Converting from radians to degrees
A
Just remember that π = 180 degrees, and input this into the equation
19
Q
Degrees to radians equation
A
Angle in degrees
———————— x2π
360
20
Q
What do we leave radian calculations in terms of?
A
π
21
Q
What is angular velocity also known as?
A
Angular frequency
22
Q
What does our measurement the radian helps measure?
A
Th angle subtended (drawn out) by an object moving in a circle
23
Q
Angular velocity/frequency symbol
A
ω
24
Q
ω
A
Angular velocity/frequency
25
Angular velocity
The rate of change of angle measured in radians per second
26
Angular velocity equation
ω = angle
———
t
27
How is the angular velocity equation altered for a full rotation of time period T?
ω= 2pi
——
T
28
Which radian measurement is used for a whole circle?
2 pi
29
Equation for relationship between period and frequency
T = 1/f
30
Angular velocity equation involving frequency
ω = 2pif
31
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
32
When whirling a hammer in a circle, describe its velocity
Will have a velocity at a tangent to the circle
33
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
34
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
35
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
36
What is constant and what isn’t in centripetal acceleration (when spinning at a constant rate)?
Magnitude = constant
Path = not constant
37
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
38
Centripetal force
Causes centripetal acceleration, which is always directed towards the centre of a circular path
39
What does a centripetal force keep an object doing?
Moving in a circle
40
What would happen to a spinning object once the centripetal force is gone?
It would accelerate in a straight line
41
Is centripetal force a type of force?
No
42
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
43
Force that provides the centripetal force during the orbit of the earth around the sun
Gravitational
44
Force that provides the centripetal force during a car cornering
Frictional
45
Force that provides the centripetal force with a child on a swing
Tensional
46
Force that provides the centripetal force with a child on a roundabout
Frictional
47
Force that provides the centripetal force during an electron orbiting a nucleus
Electromagnetic
48
Force that provides the centripetal force on a wind turbine
Tension
49
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)
50
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
51
Linear velocity on a circle equation to learn
v = 2pir/T
(2pir = circumference of a circle)
(T = time period for a full circle)
52
What does a higher radius result in for an object with circular motion? Provided what?
A faster velocity
Provided that ω is constant
53
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
54
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
55
Equation relating angular and linear velocity
v = ωr
56
Equation relating centripetal acceleration and angular velocity
a = ω^2r
57
Centripetal acceleration
Acceleration needed to keep an object moving in a circle
58
Acceleration needed to keep an object moving in a circle
Centripetal acceleration
59
Derive a = v^2/r
Rearrange v = ωr to ω = v/r and place it into a = ω^2r
a = v^2/r
60
Difference between v and ω
v = linear velocity
ω = angular velocity
61
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
62
In which direction is the acceleration of circular motion?
Towards the centre of circular motion
63
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
64
What are the 2 equations for linear velocity to learn?
V = 2pir/T
And since f=1/T,
V = 2pirf
65
Which forces make up the centripetal force in vertical circles?
Tension in the string
Weight of the object
66
Equation for centripetal force at the top of a vertical circle
Centripetal force = weight + tension
67
Equation for tension at the top of a vertical circle
Tension = centripetal force - weight
68
What is constant on all points of a vertical circle and why?
Centripetal force
v is constant
69
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
70
Equation for centripetal force at the bottom of a vertical circle
Centripetal force = tension - weight
71
Equation for tension at the bottom of a vertical circle
Tension = centripetal force + weight
72
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
73
Why does it feel like there’s more force at the bottom when spinning something around?
As there’s higher tension at the bottom
74
What is revs.min-1?
A form of frequency
75
What value do we use if something is “weightless” in a question?
a = 9.81ms-2
76
What value do we use if something is at “minimum speed” in a question?
a = 9.81ms-2
77
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
78
Degrees to radians
Degrees x 2pi/360
79
Radians to degrees
Radians x 360/2pi
80
Why is a car accelerating when moving in a circle?
Direction changing = velocity changing = accelerating
