# Laws Of Motion Class 11 Notes Physics Chapter 5 - CBSE

## What Are Laws Of Motion ?

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## Force

It is defined as a push or pull which changes or tends to change the state of rest of uniform motion or the direction of motion of the body.

## Inertia

It is the inherent property of a material body by virtue of which it cannot change by itself, its state of rest or of uniform motion.

## Momentum

It is the quantity of motion in a body. It is given by p = mv, its SI unit is kg ms–1.

## Newton’s Law Of Motion

First Law

Newton’s first law of motion states that every body continues in its state of rest or of uniform motion along a straight line, unless an external force is applied to change that state.

Second Law

Newton’s second law states that the rate of change of momentum of a body is directly proportional to the applied force.

$$\text{F}=\frac{\text{dp}}{\text{dt}} =\frac{\text{d}}{\text{dt}}(\text{mv})\\= m\frac{\text{dt}}{\text{dt}}$$

Third Law

Newton’s third law states that to every action,
there is an equal and opposite reaction.

$$\vec{\text{F}}_{\text{BA}} = -\vec{\text{F}}_{\text{AB}}$$

## Impulse

It is the total effect of a large force which acts for a short time to produce a finite charge in mometum.

Impulse = Force × Time duraction

## Apparent Weight Of Body In A Lift

• When a lift moves upwards with unifor acceleration, then apparent weight

R = m(g + a)

• When lift moves downwards with acceleration a, then apparent weight

R = m(g – a)

• During free fall (a = g)

R = m(g – g) = 0

## Law Of Conservation Of Linear Momentum

It states that in the absence of any external force, vector sum of the linear momentum of a system of particles remains constant.

## Friction

When a body moves or tends to move over the surface of another another body, a force comes into play which acts parallel to the surface of contact and opposes the relativemotion. This opposing force is called friction.

• The force of friction which comes into play between two bodies before one body actually starts moving over the other is called static friction.
• The maximum force of static friction which comes into play when a body just starts moving over the surface
of another body in called limiting friction.
• The force of friction which comes into play when a body is in a steady motion over the surface of another
body is called kinetic or dynamic friction (fc). Kinetic friction is less than limiting friction.
• Coefficient of limiting friction is the ratio of limiting friction to the normal friction.
• Centripetal Force: It is the force required to make a body move along a circular path with a uniform speed.
It always acts along the radius and towards the centre of the circular path.

$$\text{F} =\frac{\text{mv}^{2}}{\text{r}}=mr\omega^{2}\\=mr(2\pi v)^{2}\\ = mr\bigg(\frac{2\pi}{\text{T}}\bigg)^{2}$$

• Centrifugal force is a fictitious force acting radially outwards on a particle moving in a circle and is equal in
magnitude to the centripetal force.
• If fc is the coefficient of friction between tyres and road, then the maximum velocity with which the vehicle can safely take a circular turn of radius r is given by

$$v =\sqrt{\mu rg}$$

• The maximum angle with which a vehicle (in the absence of friction) can negotiate a circular turn of radius r and banked at an angle θ is is given by

$$v =\sqrt{\text{(rg tan)}\space\theta}$$

When the frictional forces are also taken into account, the maximum rate is given by

$$v =\sqrt{\text{rg}\bigg(\frac{\mu +\text{tan}\theta}{\text{1 +}\mu\text{tan}\theta}\bigg)}$$

• In order to take a circular turn of radius r with speed v, the cyclist should bend himself through an angle θ from the vertical such that,

$$\text{tan}\space\theta =\frac{v^{2}}{\text{rg}}$$