Ch.4. Forces and Newton’s laws of motion
These four equations of kinematics are also used in this Chapter:
1. vf = vi + at
2. d =
 vf  vi  .t
2
3. d = vit + ½ at2
4. vf2 – vi2 = 2.a.d
Newton’s first law of motion: Also called Law of Inertia and applies to
both moving and non moving objects. Mass is a measure of inertia.
Newton’s second law of motion: Also called Law of Acceleration.
 F = m.a (units of force is N, mass is kg and a is m/s2)
A net (unbalanced) force is required to produce a change in state of rest
or uniform straight line motion. Force is NOT required to maintain a
state of rest or motion. Therefore, there is no net force acting on an
object moving at constant velocity. If acceleration = 0, then no net force
is acting on the object and vice versa.
Newton’s third law of motion: Also called Law of Action-Reaction.
Forces always come in PAIRS.
For example, swimming, walking, foot
kicking ball, apple falling to earth, rocket blast off. Action-Reaction
forces do not act on the same object, but on different objects. That is
why they do not cancel each other. An apple and the Earth attract each
other with equal and opposite force, but we observe the apple falling
towards the earth and not vice versa. As the mass of the earth is very
large, the same force causes very little acceleration. For example if the
apple was 120 gm then the acceleration of the Earth would be around 2 x
10-25 m/s2, whereas the apple’s acceleration would be -9.8 m/s2.
Weight: is a result of the force of gravity acting on a mass. The unit of
weight is N. Due to Newton’s third law, the object presses the ground
with a weight w, and the ground presses the object with an equal and
opposite force called the normal force FN.
w = m.g (mass is in kg, and g = -9.8 m/s2)
w = 0 in outer space as there is no gravity.
If a number of forces act on an object, the net force is the vector sum
of all the forces. The forces must be resolved in to x & y components.
The acceleration vector points in the same direction as the force vector.
 Fx = sum of all x-components,  Fy = sum of all y-components,
Fx = F. cos  

ax =  Fx / m
 F =
F
x
2
 Fy 2
Fy = F. sin 
a y =  Fy / m

a =  F / m
 = tan-1(Fy / Fx)
 = tan-1(ay/ax)
Newton’s Law of Universal Gravitation:
Any two masses m1 and m2
separated by a center to center distance of ‘d’, are attracted to each
other by a gravitational force F, which is directly proportional to the
product of their masses, and inversely proportional to the square of the
distance between them. G is the universal gravitational constant which is
G = 6.67 x 10-11 N.m2 / kg2.
F
G.m1.m 2
d2
Acceleration due to gravity:
on the surface of any planet, star or
heavenly body of mass MP and radius RP is given by
gP = G.MP / RP2
Weight of any object of mass m on that planet is WP = m.gP
Calculate the acceleration due to gravity on the moon and earth.
gM =
gE =
For a satellite at a height of ‘h’ above the Earth’s surface, the centre to
centre separation is r = RE + h, so the acceleration due to gravity will be
reduced at this height to
gE = G.ME / (RE + h)2
h
ME
RE
Friction: occurs due to surface irregularities. Even highly polished
surfaces are rough at the molecular level. Friction is a force that always
acts parallel to the surface of contact, and always opposes motion.
Obviously, the amount of frictional force depends on both the objects.
Static friction: fS = S.FN, where FN is the normal force and S is the
coefficient of static friction. Static friction comes into play when you
apply a force on an object and it has not yet begun to move.
Kinetic friction: fk = k.FN, where FN is the normal force and k is the
coefficient of kinetic friction. Kinetic friction is the friction acting on an
object in motion.
Consequence of this is that friction on a planet or moon with lesser
gravity would have lesser frictional force associated with horizontal
motion. Kinetic friction is always less than static friction. This is seen in
everyday life where we observe that it is easier to slide an object that is
already in motion than to just get it to start to move. Rolling friction is
much less than sliding friction. That is why the invention of the wheel was
a great step forward!!
FN
mg.sin 

mg.cos 
An object on an incline experiences less normal force, that is, it only
experiences the vertical component of the normal force. If the angle of
the incline is , then the x & y components of weight are
Wx = W. cos (90-) = W. sin 
Wy = W. sin (90-) = W. cos 
Since friction depends on normal force, the frictional force is also
reduced. FN = W. cos When W. sin  > S. W. cos , an object will
slide down. When an object just begins to slide then tan  = S.