2.1 – Motion
Distance and displacement
Speed and velocity
Speed |
Velocity |
Scalar |
Vector |
Rate of change of distance to time |
Rate of change of displacement to time |
Velocity is a measure dependent on the motion of the observer. The relative velocity of A to B is equal to the vector subtraction of the velocity of B from the velocity of A.
Acceleration
Acceleration |
Vector |
Rate of change of velocity |
Acceleration due to gravity of any free-falling object is given by g=9.81m/s^2. This value does not depend on the mass of the object.
Take note that acceleration is a vector and thus has a direction. If we assume the upwards direction to be positive, the acceleration due to gravity would have a negative value of g=-9.81m/s^2.
Take note that acceleration is a vector and thus has a direction. If we assume the upwards direction to be positive, the acceleration due to gravity would have a negative value of g=-9.81m/s^2.
Graphs describing motion
Displacement-time graph
The slope gradient indicates the velocity.
Straight lines imply constant velocity.
Straight lines imply constant velocity.
Velocity-time graph
The slope gradient indicates the acceleration.
Straight lines imply constant acceleration.
The area under the lines indicates the change in displacement.
Straight lines imply constant acceleration.
The area under the lines indicates the change in displacement.
Acceleration-time graph
Horizontal lines imply constant acceleration.
The area under the lines indicates the change in velocity.
The area under the lines indicates the change in velocity.
Equations of motion for uniform acceleration
Projectile motion
An object is said to undergo projectile motion when it follows a curved path due to the influence of gravity.
If we assume air resistance to be negligible in a projectile motion:
- The horizontal component of velocity is constant
- The vertical component of velocity accelerates downwards at 9.81m/s^2
- The projectile reaches its maximum height when its vertical velocity is zero
- The trajectory is symmetric
The presence of air resistance changes the trajectory of the projectile by the following
- The maximum height of the projectile is lower
- The range of the projectile is shorter
- The trajectory is not symmetric
Fluid resistance and terminal speed
Air resistance limits the maximum velocity an object could attain from free-falling. For example:
- If you jump out of a plane and undergo free-falling, you will feel an upward force exerted on you by the surrounding air due to air resistance.
- As you fall faster and faster due to gravity, this upward force exerted by air becomes greater and greater until it balances your weight. At this point, the net force acting on you becomes zero, and you no longer accelerate.
- This specific velocity at which you stop accelerating during a free-fall is called the terminal velocity.
Objects as point particles
Random error |
Systematic error |
|
|
Examples:
|
Examples:
|
Free-body diagrams
Absolute uncertainty |
Fractional uncertainty |
Percentage uncertainty |
Δx |
Δx /x |
Δx/x*100% |
Calculating with uncertainties
Addition/Subtraction |
Multiplication/Division |
Power |
y=a±b |
y=a*b or y=a/b |
y=a^n |
Δy=Δa+Δb (sum of absolute uncertainties) |
Δy/y=Δa/a+Δb/b (sum of fractional uncertainties) |
Δy/y=|n|Δa/a (|n| times the fractional uncertainty) |
Physical measurements are sometimes expressed in the form x±Δx. For example, 10±1 would mean a range from 9 to 11 for the measurement.
Translational equilibrium
Newton’s laws of motion
- Line of best fit: The straight line drawn on a graph so that the average distance between the data points and the line is minimized.
- Maximum/Minimum line: The two lines with maximum possible slope and minimum possible slope given that they both pass through all the error bars.
- The uncertainty in the intercepts of a straight line graph: The difference between the intercepts of the line of best fit and the maximum/minimum line.
- The uncertainty in the gradient: The difference between the gradients of the line of best fit and the maximum/minimum line.
Solid friction
2.3 – Work, energy and power
2.4 – Momentum and impulse
Newton’s second law expressed in terms of rate of change of momentum
Impulse and force–time graphs
Conservation of linear momentum
Elastic collisions, inelastic collisions and explosions
Recommended teaching hours
out of 95 Core hours
2.2 – Forces
Vector and scalar quantities
Scalar |
Vector |
A quantity which is defined by its magnitude only |
A quantity which is defined by both is magnitude and direction |
Examples:
|
Examples:
|
Gravitational potential energy
Vector addition and subtraction can be done by the parallelogram method or the head to tail method.
When resolving vectors in two directions, vectors can be resolved into a pair of perpendicular components.
where Av = Asinθ and Ah = Acosθ
FYI
The relationships between two sets of data can be determined graphically.
Relationship |
Type of Graph |
Slope |
y-intercept |
y=mx+c |
y against x |
m |
c |
y=kx^n |
logy against logx |
n |
logk |
y=kx^n+c with n given |
y against x^n |
k |
c |
Elastic potential energy
Work done as energy transfer
Power as rate of energy transfer
Principle of conservation of energy
Efficiency