Kinematics and Dynamics Notes
KINEMATICS
Average Speed
Average speed is calculated as total distance traveled divided by the total time taken.
speed = \frac{total \ distance \ travelled}{total \ time \ taken}
Uniform Speed
Uniform speed implies that the change in distance traveled by an object is the same for every unit of time.
Time and Distance
Example:
Time = 0s, Distance = 0m
Time = 1s, Distance = 10m
Time = 2s, Distance = 10m + 10m = 20m
Time = 3s, Distance = 20m + 10m = 30m
Difference Between Distance and Displacement
Distance:
Total length covered by a moving object, regardless of direction.
Has magnitude only.
SI unit: meter (m).
Displacement:
Distance measured in a straight line from a fixed reference point.
Has both magnitude and direction.
Example:
Object moves 10m in one direction and then 2m back.
Displacement = 8m,
Distance = 10m + 2m = 12m.
Velocity
Rate of change in displacement.
SI unit: m/s.
velocity = \frac{displacement}{time \ taken}Average velocity:
average \ velocity = \frac{total \ displacement}{total \ time \ taken}
Acceleration
Object accelerates when its velocity changes.
Velocity changes with speed or direction changes (or both).
Rate of change of velocity.
SI unit: m/s². acceleration = \frac{change \ of \ velocity}{time \ taken} = \frac{V-U}{t}
Where:
V = Final velocity
U = Initial velocity
t = Time taken
Uniform acceleration is the constant rate of change of velocity.
Displacement-Time Graphs
The gradient of a displacement-time graph gives the velocity of the object.
Case 1: Object at Rest
Graph has zero gradient.
Displacement is constant.
Velocity is 0 m/s.
Case 2: Object Traveling with Uniform Velocity
Graph has a constant gradient.
Displacement increases linearly with time.
Velocity is constant (e.g., 10 m/s).
Case 3: Object Traveling with Increasing Velocity
The graph has an increasing gradient.
Velocity of the car increases.
Case 4: Object Traveling with Decreasing Velocity
The graph has a decreasing gradient.
Velocity of the car decreases.
Velocity-Time Graphs
The gradient of a velocity-time graph gives the acceleration of the object.
Case 1: Object at Rest
Velocity of the car remains at 0 m/s.
The gradient is zero.
Zero acceleration.
Case 2: Object Traveling with Uniform Velocity
Velocity of the car remains constant (e.g., 10 m/s).
Zero gradient, zero acceleration.
Case 3: Object Traveling with Uniform Acceleration
Velocity of the car increases linearly with time.
Graph has a positive and constant gradient.
Acceleration is constant.
Case 4: Object Traveling with Uniform Deceleration
Velocity of the car decreases linearly with time.
Graph has a negative and constant gradient.
Deceleration is constant.
Case 5: Object Traveling with Increasing Acceleration
The increase of velocity is increasing with time.
Graph has a positive and increasing gradient.
Acceleration increases.
Case 6: Object Traveling with Decreasing Acceleration
The increase of velocity is decreasing with time.
Graph has a positive and decreasing gradient.
Acceleration decreases.
Note: The car is still speeding up but at a decreasing rate.
Area Under Velocity-Time Graph
The area under the velocity-time graph gives the displacement.
Acceleration of Free Fall
All objects, regardless of mass/size, fall at the same acceleration due to Earth's gravity, if air resistance is negligible.
The acceleration due to gravity is constant (approximately 10 \frac{m}{s^2}).
Factors Affecting Free Fall
Gravity of Earth (approximately 10 \frac{m}{s^2}).
Air resistance.
Vector vs. Scalar Quantities
Scalar:
Physical quantity with magnitude only.
Examples: Speed, distance, mass, energy, time.
Vector:
Physical quantity with both magnitude and direction.
Examples: Displacement, velocity, acceleration, force, weight.
DYNAMICS
Non-Contact Forces
Gravitational Force:
The pull exerted by Earth's gravity on any object (e.g., weight).
Electrostatic Force:
Attractive or repulsive forces between electric charges.
Magnetic Force:
Attractive or repulsive forces between magnets.
Contact Forces
Friction:
Force that opposes or tends to oppose motion between surfaces in contact.
Air Resistance:
Frictional force exerted by air that opposes the motion of moving objects.
Normal Force:
The push exerted by a surface on an object pressing on it which is always perpendicular to the surface.
Tension:
The pull exerted by a stretched string or rope on an object attached to it.
Mass
Measure of amount of matter in a body.
SI unit: kilogram (kg).
Does not change with location or shape.
Weight
Gravitational force acting on an object that has mass.
SI unit: Newton (N).
Vector quantity with magnitude and direction. w = mg
Where:
w = weight
m = mass (kg)
g = gravitational field strength
Field
Region in which an object experiences a force.
Gravitational Field
Region in which a mass experiences a force due to gravitational attraction.
Gravitational Field Strength
Defined as gravitational force per unit mass placed at that point. g = \frac{F}{m} F = ma
Where:
F = resultant force (N)
m = mass (kg)
a = acceleration (m/s²)
Newton's First Law
Every object will continue in its state of rest or uniform motion in a straight line unless a resultant force acts on it.
If the resultant force acting on an object is zero, the object is balanced.
Inertia
Refers to the reluctance of an object to change its state of rest or motion due to its mass.
The larger the mass, the harder it will be for the object to start moving, slow down, move faster, or change direction.
Newton's Second Law
When a resultant force acts on an object of constant mass, the object will accelerate in the direction of the resultant force.
If the resultant force acting on an object is not zero, the forces are unbalanced.
F = ma
Newton's Third Law
If body A exerts a force F{AB} on body B, body B will exert an equal and opposite force F{BA} on body A.
Normal and weight forces are NOT an action-reaction pair.
Free Body Diagrams
Diagram representing all forces acting on an object.
Common forces: weight (w), normal force (N), applied force, friction, air resistance (ARA).
Friction
Contact force that opposes or tends to oppose motion between surfaces in contact.
Pros:
Enables walking without slipping.
Allows moving objects to slow down when needed.
Cons:
Cars are less efficient (by approximately 20%).
Causes wear and tear faster.
Objects Falling with Air Resistance
An object can only be in free fall if the only force acting on it is its weight.
Air Resistance:
Opposes the motion of moving objects.
Increases with the speed of the object.
Increases with the surface area (or size) of the object.
Increases with the density of air.
When air resistance acting against an object equals its weight, the object starts to travel at a constant speed known as terminal velocity. The object has zero acceleration.
Physical Quantities and Units
Physical Quantity
A physical quantity is something that can be measured.
Consists of a numerical magnitude and a unit.
Ways to Measure Length
Meter Ruler and Measuring Tape:
Meter rulers measure up to 1m.
Measuring tapes measure straight distances more than 1m.
Cloth measuring tapes measure length along a curved surface.
Digital Calipers:
Used to measure internal and external diameters of objects accurately (up to 2 decimal places in mm).
Typical range: 0-15cm.
Digital Micrometer Screw Gauge:
Used to measure objects that are too small for calipers.
Most precise (up to 3 decimal places in mm).
Typical range: 0-2.5cm.
Measurement of Time
SI unit: seconds (s).
Pendulum: Used to measure time; each complete to-and-fro motion is one oscillation (called a period).
Types of Errors
Parallax error
Random error (human reaction time)
Base SI Units
Quantity | Unit | Symbol |
|---|---|---|
Length | meter | m |
Mass | kilogram | kg |
Time | second | s |
Electric current | ampere | A |
Temperature | Kelvin | K |
Amount of substance | mole | mol |
Metric Prefixes
Prefix | Symbol | Value |
|---|---|---|
tera- | T | 10^{12} |
giga- | G | 10^9 |
mega- | m | 10^6 |
kilo- | k | 10^3 |
deci- | d | 10^{-1} |
centi- | c | 10^{-2} |
milli- | m | 10^{-3} |
micro- | μ | 10^{-6} |
nano- | n | 10^{-9} |