Laws Of Motion Class 11 Notes Physics Chapter 5 - CBSE
Chapter : 5
What Are Laws Of Motion ?
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,
$$\text{tan}\space\theta =\frac{v^{2}}{\text{rg}}$$
