Introduction: Motion, force and laws of motion

A Reference Point is used to describe the location of an object. An object can be referred through many reference points.

Origin –

The reference point that is used to describe the location of an object is called Origin.For Example, a new restaurant is opening shortly at a distance of 5 km north from my house. Here, the house is the reference point that is used for describing where the restaurant is located.

What is motion?

If the location of an object changes with time the object is said to be in motion.

Distance: The magnitude of the length covered by a moving object is called distance. It has no direction.

Displacement: It is the shortest distance between two points or the distance between the starting and final positions with respect to time. It has magnitude as well direction. Displacement can be zero, but distance cannot.

Negative Displacement and Positive Displacement

Here, displacement of object B is negative
ΔB = B_f − B₀ = 7–12 = – 5
A negative sign indicates opposite direction here.
Also, displacement of object A is positive
ΔA = A_f − A₀ = 7– 0 = 7

Scalar and Vector Quantities

• A vector quantity describes the magnitude as well as the direction.
• A scalar quantity describes a magnitude or a numerical value.

Difference between distance and displacement

Uniform motion – When an object travels equal distances in equal intervals of time the object is said to have a uniform motion.

Non-uniform motion- When an object travels unequal distances in equal intervals of time the object is said to have a non-uniform motion.

Average Speed – If the motion of the object is non-uniform then we calculate the average speed to signify the rate of motion of that object.

Velocity- To describe the rate of motion in a direction the term velocity is used. It is defined as the speed of an object in a particular direction.

Velocity= Displacement/Time
SI Unit: meters
Symbol Representation: M/s or ms^(-1)

Instantaneous speed and instantaneous velocity

• The magnitude of speed or velocity at a particular instance of time is called Instantaneous Speed or Velocity.

• In case of uniform motion the velocity of an object remains constant with change in time. Hence, the rate of change of velocity is said to be zero.

Acceleration

In case of non-uniform motion the velocity of an object changes with time. This rate of change of velocity per unit time is called Acceleration.
Acceleration = Change in velocity/ Time taken
SI Unit: m/s²

• Uniform Acceleration – An object is said to have a uniform acceleration if , It travels along a straight path  and Its velocity changes (increases or decreases) by equal amounts in equal time intervals.
• Non – Uniform Acceleration – An object is said to have a non-uniform acceleration if, Its velocity changes (increases or decreases) by unequal amounts in unequal time intervals.
• Acceleration is also a vector quantity. The direction of acceleration is the same if the velocity is increasing in the same direction. Such acceleration is called Positive Acceleration.
• The direction of acceleration becomes opposite as that of velocity if velocity is decreasing in a direction. Such acceleration is called Negative Acceleration.
• De-acceleration or Retardation – Negative acceleration is also called De-acceleration or Retardation.

Graphical Representation of Motion

1. Distance – Time Graph

• It represents a change in position of the object with respect to time.
• The graph in case the object is stationary (means the distance is constant at all time intervals) – Straight line graph parallel to x = axis
• The graph in case of uniform motion – Straight line graph
• The graph in case of non-uniform motion – Graph has different shapes

2. Velocity – Time Graphs

• Constant velocity – Straight line graph, velocity is always parallel to the x-axis
• Uniform Velocity / Uniform Acceleration – Straight line graph
• Non-Uniform Velocity / Non-Uniform Acceleration – Graph can have different shapes

3. Equations of Motion

The equations of motion represent the relationship between an object’s acceleration, velocity and distance covered if and only if,

• The object is moving on a straight path
• The object has a uniform acceleration

Three Equations of Motion

1. The Equation for Velocity – Time Relation
v = u + at

2. The Equation for Position – Time Relation 
s = ut + 1/2 at²

3. The Equation for the Position – Velocity Relation
2a s = v² – u²
Where,
u: initial velocity
a: uniform acceleration
t: time
v: final velocity
s: distance traveled in time t

Uniform Circular Motion

If an object moves in a constant velocity along a circular path, the change in velocity occurs due to the change in direction. Therefore, this is an accelerated motion.

Consider the figure given below and observe how directions of an object vary at different locations on a circular path.

When an object travels in a circular path at a uniform speed the object is said to have a uniform circular motion.

Non-Uniform Circular Motion

When an object travels in a circular path at a non-uniform speed the object is said to have a non-uniform circular motion

Examples of uniform circular motion:

• The motion of a satellite in its or
• The motion of planets around the sun

Velocity of Uniform Circular Motion
Velocity = Distance/ Time = Circumference of circle / Time
v = 2πr/ t
where,
v: velocity of the object
r: radius of the circular path
t: time taken by the object

Force

A force is an effort that changes the state of an object at rest or at motion. It can change an object’s direction and velocity. Force can also change the shape of an object.

Balanced force

When balanced forces are applied to an object, there will be no net effective force acting on the object. Balanced forces do not cause a change in motion.

Unbalanced force

When Unbalanced forces acting on an object change its speed and/or direction of motion. It moves in the direction of the force with the highest magnitude.

Net force

When multiple forces act on a body, they can be resolved into one component known as the net force acting on the object. For Example:

Friction

The force that opposes relative motion is called friction. It arises between the surfaces in contact. Example: When we try to push a table and it does not move is because it is balanced by the frictional force.

First Law of Motion or the law of inertia

A body continues to be in the state of rest or uniform motion in a straight line unless acted upon by an external unbalanced force. The First Law is also called the Law of Inertia.

Inertia

Basically, all objects have a tendency to resist the change in the state of motion or rest. This tendency is called inertia. All bodies do not have the same inertia.

Inertia depends on the mass of a body. Mass of an object is the measure of its inertia. More the mass more inertia and vice versa.

Inertia and Mass

• The inertia of an object is dependent upon its mass.
• Lighter objects have less inertia, that is, they can easily change their state of rest or motion.
• Heavier objects have large inertia and therefore they show more resistance.
• Hence ‘Mass’ is called a measure of the inertia of an object.

Momentum

Impacts produced by objects depend on their mass and velocity. The momentum of an object is defined as the product of its mass and velocity. p = mv. Vector quantity, has direction and magnitude.

Second Law of Motion

The rate of change of momentum of an object is directly proportional to the applied unbalanced force in the direction of the force.
⇒Δp/t α ma
⇒F α ma
⇒F = kma
For 1 unit of force on 1 kg mass with the acceleration of 1m/s2, the value of k = 1.
Therefore, F = ma.

Concept of system

• The part of the universe chosen for analysis is called a system.
• Everything outside the system is called an environment.
• For example, a car moving with constant velocity can be considered a system. All the forces within the car are internal forces and all forces acting on the car from the environment are external forces like friction.

Conservation of momentum

• The total momentum of an isolated system is conserved.
• Isolated system net external force on the system is zero.
• Example: Collision of 2 balls A and B.
  
  m_AU_A+m_BU_B=m_AV_A+m_BV_B

Third Law of Motion

Newton’s 3rd law states that every action has an equal and opposite reaction. Action and reaction forces are equal, opposite and acting on different bodies.