Newton's laws of motion

3. Whilemost peopleknowwhat
Newton'slawssay, many people
do not knowwhat they mean(or
simply do not believe what they
mean).

4. NEWTON’S LAWS OF MOTION:
1} LAW OF INERTIA
2} F = M * A
3} ACTION - REACTION

5. NEWTON’S LAWS OF MOTION:
 1st Law – An object at rest will
stay at rest, and an object in
motion will stay in motion at
constant velocity, unless acted
upon by an unbalanced force.
 2nd Law – Force equals mass times
acceleration.
 3rd Law – For every action there
is an equal and opposite reaction.

6. 2ND LAW

7. 2ND LAW
The net force of an object is
equal to the product of its mass
andacceleration, or F=ma.

8. LINEAR MOMENTUM
The concept of linear momentum is extremelyimportant in
physics. Whenever we examine a moving object, we must
consider both its mass and velocity because the quantity
of motion possessed by the body depends upon these two
factors.

9. LINEAR MOMENTUM
The linear momentum of abody of mass m
travelling with velocity v is defined as the
product of its mass and velocity.
Thus, linear momentum p=m v
Since mass is a scalar quantity and velocity is a
vector quantity , their product, i.e. Momentum is a
vectorquantity. The direction of momentum is the
direction of velocity.

10. S I . UNIT OF MOMENTUM
We have learnt that momentum
is the product of mass and
velocity. The S I Unit of mass
is kg and the S I Unit of
velocity is m/s. So the, S I
Unit of Momentum is kilogram
meter per second which is
written as kg m/s.

11. EXAMPLES:
 We know that a cricket ball is heavier then a tennis ball. Suppose we
throw both, a cricket ball and tennis ball with the same speed. It is
found that more force is required to stop the cricket ball [which has
more mass] and less force is required to stop the tennis ball [which
has less mass]. It can be concluded that if twobodies of different
masses are moving with same speed or velocity, the force needed
the heavier body is more than that for required for the lighter body.

12.  We now throw two cricket balls of the same mass with different
speeds or velocities. It is found that more force is required to stop that
cricket ball which is moving with a higher velocity and less force is
required to stop the cricket ball moving with a lower velocity. It can
concluded that if two bodies of the same mass are moving with
different velocities, the force needed to stop the faster moving body is
more than that required for the slower moving body. So , the force
needed to stop a moving body is directly proportional to its mass and
its velocity. This gives us the term known as “momentum”.

13.  In cricket, a fielder moves his arms
backwards in the direction of ball while
taking a catch: we all have observed that in
cricket, a fielder moves his arms backwards
in the direction of ball while taking a catch
. He or she does so as to decrease the
rate of change of momentum by increasing
the time . In doing so, the entire momentum
of the ball is reduced in zero in a long
time interval. In other words, the rate of
change of momentum is small. As a result,
according to Newton’s second law of motion,
the fielder has to apply a small force on
the ball. In reaction, the ball also applies
less force and the palms of the player are
not injured. If a ball is stopped suddenly,
then the entire momentum of the ball will be
reduced to zero in a very short time
interval in which will cause a larger rate of
change of momentum. As a result, the

14.  Car passengers are advised to wear seat belts:
During a car accident, the car stops
suddenly. The seat belts worn by the
passengers of the car prevent from falling
forward suddenly. It enables the entire
momentum of the passengers to be reduced
to zero in a long time interval. In other
words, the rate of change of momentum is

15. MATHEMATICAL FORMULATION OF SECOND
LAW OF MOTION
Consider a body of mass m having an initial
velocity u. Suppose a force F acts on this body for time t. Let the final
velocity of the body be v.
Initial momentum of the body [p i]=mu
Final momentum of the body [p f]=m v
Change in momentum =p f-pi=m v-mu
=m(v-u)
Rate of change of momentum
=change in momentum
time taken

16. =m(v-u)
t … (i)
We know, v= u + at (equation of motion)
:. a= v-u
t …(ii)
Putting the value of (ii) in (i), we get
Rate of change in momentum =ma
According to Newton’s second law of motion,
F α rate of change of momentum
:. F α m* a
The relation F α m*a can be turned into an equation by
putting in a constant k.
Then F = k*m*a …(iii)

17. [ where k is a constant which converts a proportionality into an equality]
Now, we find the unit of force in such a manner that
we can get rid of the constant of proportionality . The S I
Unit of force is newton (N).
We find, one newton as that force which when
acting ona mass of 1 kg produces in it an
acceleration of 1 m /s2 in its own direction,
i.e. when m=1 kg, a= 1 m/s2 then F=1 N
1 N= 1 kg m/s 2
Let us substitute these values in equation (iii), we get
1 N = k* 1 kg* 1 m/s2
k=1 [Newton is equivalent to kg m/s2]

18. Therefore, F=ma [for
k=1]
This equation, i.e. F=ma is taken to be
the statement
of Newton’s second law of motion in the
mathematical
form.
The second law of motion gives us the
method to
measure force. If the mass of a body
and its acceleration
due to a force are known, we can measure the
force acting on

19. PROBLEMSUMS:
 Calculate the momentum of a toy car weighing 200g and
moving with a velocity of 5 m/s
Solution: Mass of the toy car =200 g
=200/1000 kg
Velocity of the toy car (v) =5 m/s
Momentum = ?
By using formula
Momentum, p = m * v, we get
p = o.2 kg * 5 m/ s
p = 1 kg m/s

20.  What is the acceleration produced by a force of 12 N exerted on an
object of mass 3 kg?
Solution: Force ( F ) = 12 N
Mass ( m ) = 3 kg
Acceleration ( a) = ?
By using the formula, F = m*a, we get
12 N = 3kg * a
a = 12 N= 12 kg m/s2
3 kg 3 kg
a =4 m/s2
Thus , the acceleration producedin an object is 4 m/s2.

21.  What force would be needed to produce an acceleration of
4 m/s 2 on a ball of mass 6 kg?
Solution : Acceleration ( a ) = 4m/s2
Mass ( m) = 6 kg
Force ( F ) = ?
By using the formula , F = m*a, we get
F = 6 kg * 4 m/s2
F = 24 kg m/s2
= 24 N
So , a force of 24 N is required

22.  Which would require a greater force –
accelerating a 2 kg mass at 5 m/s2 or a 4 kg
mass at 2 m/s2 ?
Solution : From equation , F = m*a we get
m1 = 2 kg ; a1 = 5
m/s2
m2 = 4 kg ; a2 = 2m/s2
Thus F 1 = m 1 a1 = 2 kg * 5 m/s2 = 10 N
F 2 = m2 a2 = 4 kg * 2 m/s2 = 8 N
F1 > F2
Thus , accelerating a 2 kg mass at 5 m/s2 would
require a

23. CONCLUSION :
Thus we can conclude that F = m*a and p = m*v
this means that force equals mass times
acceleration
and momentum equals mass times velocity
respectively.

24. Purvi.P.Subedarpage