Kinematics
Distance
X
Total length travelled (direction doesn’t affect)
Displacement
X
X
Change in position (vector: magnitude + direction)
Can be positive, negative or 0
Speed
X
X
X
Distance moved/time
S = ½ (u+v)t
S = ut + ½ at2
V = u + at
V2 = u2 + 2as
Average speed = total distance/time
Instantaneous speed = speed at 1 specific time (gradient of d-t graph)
Velocity
X
X
X
X
X
Change in displacement/change in time
Changing velocity: speed/direction changes
Average velocity = total displacement/total time
Uniform velocity = motion in straight line with constant speed, no acceleration
Instantaneous velocity = velocity at 1 specific time
*Instantaneous speed = magnitude of instantaneous velocity, but average speed  magnitude of average velocity
Acceleration
X
X
X
X
X
X
Change in velocity/change in time
or
(v-u)/t
Speed up
Slow down
Change direction
Deceleration = decrease in velocity every second
In a v-t graph, acceleration = gradient
*Acceleration of Free Fall
X
X
X
Subjected to force of gravity alone, assume no air resistance
10m/s2 – constant for all materials, sizes, shapes, masses
Applied for compact objects with small surface area
X
When projected upwards, speed of object decreases at a rate of 10m/s 2
*Fan: circular motion, always accelerating because the direction keeps changing
Graphs
Graph (draw it!)
Distance-time/displacement-time
Constant, uniform speed
Speed-time/velocity-time
Constant acceleration
Acceleration-time
 acceleration (at constant
rate)
 speed, constant acceleration
 acceleration
 acceleration (at  rate)
 speed, negative acceleration
 acceleration
 acceleration (at  rate)
At rest
Constant speed
Constant acceleration
Didn’t move at all
At rest
Constant speed
Forces
X
Vector quantity = magnitude + direction
Contact Force
Require physical contact between the 2 objects for force to be applied
Examples:
 Frictional Force
 Applied Force
 Air Resistance
 Tension Force
 Normal Force
 Spring Force
Non-contact force
Do not require physical contact between
the 2 objects for the force to be exerted
Examples:
 Gravitational Force
 Magnetic Force
 Electrical Force
Newton’s Laws
1. When forces acting on a body are balanced (equal and opposite)
Fnet = 0, a = 0m/s2
X
X
2.
3.
Object at rest: v = 0m/s, stays at rest
Object in motion: v  0m/s, stays in constant motion at uniform velocity
When body experiences a net force  0 (forces are not balanced and equal)
It will accelerate and slow down/speed up/change direction
Action is equal and opposite to reaction
Object in equilibrium: normal = gravity
F = ma
Free Body Diagram
X
X
X
Simplification
Assumptions:
X
X
X
Translational motion , not rotational
Longer arrow = greater force
G = 10N/kg
Mass (kg)
X
Quantity of matter in object
Weight (N)
X
X
W = mg
Force upon object due to gravity
Tension
X
X
X
X
Pulling force
Unstretched rope – 0 tension
Stretched rope – tension = weight
Very stretched – too high tension, rope snaps
Normal
X
X
Body of interest (in equilibrium)
Body of interest is not too long
Gravity
X
Air resistance
Treat moving object as a mass concentrated at a single point
When 2 bodies interact by pressing on each other
Always perpendicular to contacting surfaces
Gravitational pull
Friction
X
X
X
X
When 2 bodies move/attempt to move
X
X
X
Prevents motion (eg sliding)
1 body opposes motion of other body
3rd body must provide external force to cause motion
On rough surfaces only, smooth surfaces = negligible friction
Dependent on
Not dependent on
Nature of surface (smooth/rough)
Area of contact
Force pressing on surface
Area of contact
Produces motion (eg wheels of a car)
Reducing friction
X
X
X
X
Lubricate surfaces with oil/grease
Use ball bearings/rollers
Separate surfaces with a cushion of air
Fluid Friction
X
X
Air resistance, water resistance
Total surface area
X
X
X
 Surface area,  Resistance
Eg parachute
Speed of motion of object
X
X
 Speed,  Resistance
Eg sprinting vs walking
Inertia
X
X
X
Property of all objects with mass
Body will resist change to original motion unless acted on by net force
When explaining: Original state, Action, Inertia, Link back, Answer
Falling Parachutes
Free-fall
X
Fnet = mg (a = g = 10m/s)
Non free-fall
X
X
Fnet = mg – R
Air resistance is dependent on surface area and speed, so V, R 
Initial
X
X
Velocity is approximately zero/very small, so V = 0, R = 0
X
X
X
As the body accelerates V, R  until R = mg
X
X
X
X
V, R  until R=mg
Fnet = mg (a = g = 10m/s), almost free-fall
Intermediate
Fnet = mg-R , with R increasing, Fnet is smaller
Acceleration decreases
Final
Fnet = mg-R = 0
Acceleration = 0
Terminal velocity!
Parachute!
X
X
X
X
X
X
X
X
X
Accelerates from rest, speeding up due to positive net force
A decreases with time as he speeds up
When AR = mg, Fnet = 0, so A = 0
Parachute opens!
Surface area increases significantly
SA , AR 
Decelerate (decrease in velocity)
AR 
Mg = R, new terminal velocity
Vectors
Vector Addition
X
X
X
Identify forces by drawing FBD
X
Non-collinear = must draw vector triangle or parallelogram 
1. Use a suitable BIG scale to represent each tension in magnitude and direction (eg 1 cm to 50N)
Net force = sum of all forces, depending on magnitude and direction
Collinear  (acting along a straight line) = just add and subtract 
2. Translate Tension A parallel to its original direction
3. Resultant/net force is found by joining the triangle
4. Record resultant force by measurement
Vector Resolution
Components of Vectors
X
X
All vectors can be split/reduced to their horizontal and vertical components (perpendicular)
Using trigo, the magnitude and direction of each of these components can be calculated
Y component (Vertical) : Rsin
X component (Horizontal) : Rcos
R

1.
2.
Change both vectors into their horizontal and vertical components
Construct the following table:
Horizontal Component (X)
Vertical Component (Y)
Vector 1
Rcos
Rsin
Addition
Vector 2
R2cos2
R2sin2
Resultant
Net Horizontal Force
Net Vertical Force
Resultant Force = √(Net Horizontal Force)2 + (Net Vertical Force)2
Angle of Resultant Force= tan-1 (Net Vertical Force/ Net Horizontal Force)
Addition
Work
X
X
Applied force on object, object moves a certain distance
W = Fd
Work done (J) = Force (N) x distance/displacement (m)
X
1 Joule = 1Nm
Energy
X
X
Capacity to do work (J)
Principle of conservation of energy – pendulum
X
X
But in real life: frictional forces, lost as thermal energy etc
Mechanical energy: energy possessed by an object due to its motion/stored energy
Ek = ½ mv2
Ep = mgh
X
Kinetic energy (J) = ½ mass (kg) x velocity2 (m/s)
X
X
Faster/heavier =  Ek
Gravitational Potential energy (J) = mass (kg) x gravity (10N/kg) x height (m)
Power
X
X
X
Rate of work done/rate of energy conversion
1 Watt = 1 Joule/sec
Force x velocity (if it’s constant)
P = W/t or E/t
= F x m/s
X
High power/powerful means doing the same amount of work in less time, or more work in the same amount
of time
Efficiency
Output x 100%
Input
Moments
X
X
X
X
Moment = Fd
Turning effect of forces
Result of application of force on an object, a certain distance away from pivot
Pivot = point which doesn’t move, point of rotation/support, fulcrum
Moment (Nm) = Force (N) x Perpendicular distance (m)
o *Distance from force to pivot, which is perpendicular to the force
Steps to Doing Moment Questions
1. Indicate the pivot point: Draw a small circle at pivot point; label as P; “Taking the pivot point about P”
2. Draw in all the forces, find out the forces (__ N)
3. Draw perpendicular lines to join the pivot and the force lines
4. Find out the length of these perpendicular lines
5. Moment = Force X perpendicular distance
6. Put them into the equation Tnet = + CW – ACW
7. Take the larger number (CW/ ACW) and subtract the smaller number
8. The end result will be the moment, in the direction of the larger moment (CW/ ACW)
Centre of Gravity
X
X
Point of body through which the whole body weight acts through
Centre of mass = point of body through which the whole body concentrates
X
X
X
X
Uniform body – midpoint
Non-uniform – heavier/more massive part
Hollow – may not lie within body
To keep a body in a balanced, equilibrium position without any turning effect:
X
X
Total clockwise moment = total anticlockwise moment
Total upward force = total downward force
Stability
X
X
X
X
Ability of an object to return to its original position after it has been displaced slightly
CG must be within its support base in order to stay in equilibrium – if not it’ll topple over!
Stable body rotates back to its original support base
To increase stability:
X
X
Lower CG
Increase base area
X
Eg toys: place heavyweights at base (like lead), broad base
Stable
Unstable
Stable equilibrium means object will Unstable equilibrium means object
revert to equilibrium if slightly
does not revert back to equilibrium
disturbed
if slightly disturbed
- CG (weight line) stays within
- continues to move away from
the original base area
original position after being
displaced
- CG (weight line) moves out of
original base area when
displaced
Neutral
Neutral equilibrium means object
does not have the tendency to do
anything after being disturbed.
- CG will remain at the same
position even when displaced