Revision: Laws of Motion JEE Main Laws of Motion

Aristotle's statement: “An external force is required to keep a body in uniform motion”.

"If no force is acting on a body, its velocity does not change, i.e., the body does not accelerate. In other words, if a body is stationary, it will remain stationary. If it is in motion, it will continue moving with the same velocity and in the same direction."

or

"An object continues to remain at rest or in a state of uniform motion along a straight line unless an external unbalanced force acts on it."

or

"Every inanimate object continues to be in its state of rest or of uniform unaccelerated motion unless and until it is acted upon by an external, unbalanced force."

"The rate of change of momentum is proportional to the applied force, and the change of momentum occurs in the direction of the force."

Newton’s second law of motion states that the rate of change of momentum is directly proportional to force applied and takes place in the direction of the force.

"Every action force has an equal and opposite reaction force which acts simultaneously."

The concise law statement is: "To every action (force), there is an equal and opposite reaction (force)."

"Friction between two bodies in contact when one body is rolling over the other, is called rolling friction."

The force acting on a particle performing uniform circular motion along the radius and directed towards the centre of the circle is called the centripetal force.

The mathematical form of centripetal force is:

F = `mv^2/r`

where:

F = centripetal force,

m = mass of the object,

v = speed or velocity, and

r = radius

Friction between two surfaces in contact when one body is actually sliding over the other body is called kinetic friction or dynamic friction.

or

The force of friction that comes into play when a body is in a steady state of motion over another surface is called the force of kinetic friction.

\[\vec F\] = m \[\frac{d\vec{\mathrm{v}}}{dt}\] = m\[\vec a\] ... (for constant mass)

Thus, if \[\vec F\] = 0, \[\vec v\] is constant. Hence, if there is no force, velocity will not change. This is nothing but Newton's first law of motion.

General Form: \[\vec F\] =\[\frac{d\vec{p}}{dt}\]

For Constant Mass: \[\vec F\] = m\[\vec a\]

Momentum: \[\vec p\] = m\[\vec v\]

\[\vec{F}=\frac{d\vec{p}}{dt}=\frac{d\left(m\vec{\mathrm{v}}\right)}{dt}\]

μₖ = Fₖ/N

The coefficient of kinetic friction is defined as the ratio of force of kinetic friction to the normal reaction between the two surfaces in contact.

Fₖ = μₖ N

Where:

• Fₖ = Force of kinetic friction
• μₖ = Coefficient of kinetic friction (constant of proportionality)
• N = Normal reaction between the two surfaces in contact