Laws of Motion - Revision Notes

CBSE Class XI PHYSICS

Revision Notes

CHAPTER 5

LAWS OF MOTION

The law of inertia
Newton’s first law of motion
Newton’s second law of motion
Newton’s third law of motion
Conservation of momentum
Equilibrium of a particle, Laws of Friction
Circular motion

1. Aristotleís view that a force is necessary to keep a body in uniform motion is wrong. A force is necessary in practice to counter the opposing force of friction.

2. Galileo extrapolated simple observations on motion of bodies on inclined planes, and arrived at the law of inertia. Newtonís first law of motion is the same law rephrased thus: ìEverybody continues to be in its state of rest or of uniform motion in a straight line, unless compelled by some external force to act otherwiseî. In simple terms, the First Law is “If external force on a body is zero, its acceleration is zero”

3. Momentum (p ) of a body is the product of its mass (m) and velocity (v) :p = mv

4. Newtonís second law of motion :

The rate of change of momentum of a body is proportional to the applied force and takes place in the direction in which the force acts. Thus $F = K \frac{d p}{d t} = k m a$

where F is the net external force on the body and a its acceleration. We set the constant of proportionality k = 1 in SI units. Then

The SI unit of force is newton : 1N = 1 Kg m $s^{- 2}$ .

(a) The second law is consistent with the First Law (F = 0 implies a = 0)

(b) It is a vector equation

(c) It is applicable to a particle, and also to a body or a system of particles, provided Fis the total external force on the system and a is the acceleration of the system asa whole.

(d) F at a point at a certain instant determines a at the same point at that instant. That is the Second Law is a local law; a at an instant does not depend on the history of motion.

5. Impulse is the product of force and time which equals change in momentum. The notion of impulse is useful when a large force acts for a short time to produce a measurable change in momentum. Since the time of action of the force is very short, one can assume that there is no appreciable change in the position of the body during the action of the impulsive force.

6. Newtonís third law of motion:

To every action, there is always an equal and opposite reaction In simple terms, the law can be stated thus :

Forces in nature always occur between pairs of bodies. Force on a body A by body B is equal and opposite to the force on the body B by A.

Action and reaction forces are simultaneous forces. There is no cause-effect relation between action and reaction. Any of the two mutual forces can be called action and the other reaction. Action and reaction act on different bodies and so they cannot be cancelled out. The internal action and reaction forces between different parts of a body do, however, sum to zero.

7. Law of Conservation of Momentum

The total momentum of an isolated system of particles is conserved. The law follows from the second and third law of motion.

8. Friction

Frictional force opposes (impending or actual) relative motion between two surfaces in contact. It is the component of the contact force along the common tangent to the surface in contact. Static friction opposes impending relativemotion; kinetic frictionopposes actual relative motion. They are independentof the area of contact and satisfy the following approximate laws: $\begin{matrix} f_{s} f_{s max} s^{R} \\ f_{k} K^{R} \end{matrix}$

$μ_{s}$ (co-efficient of static friction) and $μ$ k (co-efficient of kinetic friction) are constants characteristic of the pair of surfaces in contact. It is found experimentally that $μ$ k is less than $μ$ s

Quantity	Symbol	Units	Dimensions	Remarks
Momentum	P	Kg m $S^{- 1}$ or Ns	$[M L T^{- 1}]$	Vector
Force	F	N	$[M L T^{- 2}]$	F=m a Second Law
Impulse		Kg m $S^{- 1}$ or Ns	$[M L T^{- 1}]$	Impulse =force $\times$ time=change in momentum
Static friction	f,	Ns	$[M L T^{- 3}]$	$f_{,} ⩽ μ_{s} N$
Kinetic friction	f,	N	$[M L T^{- 3}]$	$f_{,} = μ_{s} N$