Laws of Motion Notes

1. Force and Inertia

• Inertia – Inertia is a property of the body due to which body oppose the change of itself its state. The inertia of a body is measured by the mass of the body. Heavier the body greater force is required to change its state.

• Force- A force is a push or a pull which changes or tends to change the state of rest or uniform motion. Force is a vector quantity.

1. Newton’s laws of motion

• Newton’s first law of motion- It states that if the net external force on a body is zero, then the body remains at rest or move with a constant velocity. It defines the inertia hence it is also known as the law of inertia.
• Newton’s second law of motion- Newton’s second law of motion gives the definition of force. It states that the acceleration of an object is directly proportional to the net force acting on it and is inversely proportional to its mass.

• Newton’s third law of motion- It states that to every action there is an equal and opposite reaction.

Momentum- Momentum of a moving body is defined as the product of mass and the velocity of the body. 

, where m is the mass of the body and v is the velocity.

Impulse- When a large force act for an extremely short duration then the total effect of the force is known as the impulse.

Conservation law of Momentum- According to the conservation of momentum, the net change in the linear momentum in the absence of external force is zero.

Application of Conservation of Momentum

• The recoil of a gun

The system of gun and bullet is work on the law of conservation of momentum. Before firing both gun and bullet are at rest, therefore momentum of the system is zero. When the bullet is fired the bullet moves forward and gun recoils back. Since the mass of the gun is very large as compared to the mass of the bullet, therefore the recoils velocity is very small as compared the velocity of the bullet.

• Motion of rockets

Rockets are work on the law of conservation of momentum. In rocket hot gases produced by burning of fuel rush out with a large momentum, Due to this, rocket gain an equal and opposite momentum. This momentum enables the rockets and jet engines with very high velocities.

• The man and the boat

Initially, the total momentum of the man and boat is zero. As the man jumps from the boat to the shore, he gains momentum in the forward direction. To conserve momentum, the boat also gains equal momentum in the opposite direction. So the boat slightly moves backward.

Equilibrium of a Particle- A particle will be in equilibrium only when the net external force acting on them is zero. So, the particle will be either rest or uniform motion.

e.g. As shown below there are two objects A is placed on a surface.

Object A will be equilibrium when the net external force on the body is zero.

1. Common Force in Mechanics

Friction- Friction is a contact force that opposes the relative motion or tendency of relative motion of two bodies. It is self-adjusting in nature.

e.g Let the force F is applied on an object which is placed on a plane surface.

Friction force is, , where N is the Normal force and is the coefficient of friction force.

Types of friction

• Static Friction – Static friction is a type of friction force that acts on a body when there is no relative motion between the object and the surface.

Static friction force is, , where is the coefficient of static friction, N is the normal force

• Kinetic Friction- Kinetic friction is a type of friction that oppose relative motion between surfaces in contact. It is also known as sliding friction.

Kinetic friction force is, , where is the coefficient of kinetic friction, N is the normal force.

• Rolling Friction- Rolling friction is a type of friction that resist the motion of the body when body rolls on the surface. It is also known as sliding friction.

Rolling friction force is, , where is the coefficient of rolling friction, N is the normal force.

Angle of friction

The angle of friction is defined as the angle between the normal reaction N and the resultant of friction force f and the normal reaction.

Angle of friction,

1. Circular Motion

If an object moves in a circular path, then the motion of the object is known as circular motion.

When a body is moving in a circular path it experiences a force which is acts toward the radius of the circular path. This force is known as the centripetal force. Centripetal force is required to move a body on a circular path.

Centripetal Force, , where v is the velocity of the object and r is the radius of the circular path.

Types of Circular Motion

Non-Uniform Circular Motion- When an object follows a circular path, but the speed is not constant then the motion of the object is known as non - uniform circular motion.

In a non-uniform circular motion, the net acceleration of the moving body has two components.

1. Radial acceleration- Radial acceleration is due to change in the direction of the velocity.
2. Tangential Acceleration-Tangential acceleration is due to change in the magnitude of the velocity.

Net acceleration of the object is,

Uniform Circular Motion- When an object follows a circular path at a constant speed, the motion of the object is known as the uniform circular motion.

Application of Uniform Circular Motion

• Banking of Roads

In a circular path, the roads are banked at some angle, so that the vehicle can get the required centripetal force.

Maximum velocity with which a car can take a circular turn without slipping is, , where is the coefficient of friction force between the tires of the car and the road, R is the radius of the circular path.

If a vehicle moves on a curved track of radius r with maximum speed v, the track is banked through an angle θ is, 

• Satellite orbiting around the earth

When a satellite is orbiting around the earth in a circular orbit then to move around the circular path the required centripetal force is provided by the gravitational force between them.

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