As we’ve studied earlier, that a force can
change state of motion. When we talk about state of motion it is velocity
vector. And change in velocity is caused by acceleration. So we can simply state whenever a force is
applied. it causes, acceleration. And acceleration implies change in velocity. As we’ve studied earlier also that a velocity
is represented by 2 parameters, one is its magnitude and other is its direction. In both the cases whether magnitude changes
or acceleration, causes change in direction. In both cases we say the state of motion of
body is changing. Say for example if there’s a body of mass
m moving with a velocity vector v. it is moving in a straight line. In this process if we apply an external force
f onto it, due to the force, this velocity magnitude will increase as force is applied
in the direction of velocity, it’ll cause the body to speed up. In this situation we can say the magnitude
of velocity is, increasing. However the direction in this situation is
not going to change because force is applied in the direction of velocity so it’ll only
increase the speed. Or it’ll increase the magnitude of velocity. But if we consider another case, in which
say, we’re having a body of mass m it is moving with a velocity vector v. if we apply
a force which is perpendicular to the motion of velocity. Force is also a vector quantity, if we consider
the direction of force which is perpendicular to velocity. You can see, it is not going to change the
speed due to this force the direction is going to change, it’ll bend, in the direction
of force. It depends on how large the mass of body is,
which is going to decide, how fast the body will take a turn. If it is a light weight body, very soon it’ll
take a turn. If it is very heavy, because of inertia, it’ll
gradually take a turn in a large radius of curvature. So you can simply state in this situation
when force is applied in a perpendicular direction to the motion, you can say, direction of. Velocity vector is, changing. There are 2 effects, which a force can cause
in a state of motion of a body. That is, a parallel force. Causes. change in magnitude of. velocity. And a normal force which is applied perpendicular
to the direction of motion it causes. change in direction of, velocity vector. So always keep in mind, that a force can change
state of motion in 2 ways, if force is acting in the direction of velocity it’ll change
the magnitude of velocity. If force is applied in direction normal to
velocity that is at right angle to the direction of motion, then it’ll not change the magnitude
it’ll only change the direction of velocity. To understand the concept in a better way,
we just take up a practical illustration. Say we’re having a cordinate system x-y. In this system, the particle starts from point
a. and say it moves along this path, and reaches
point b. in this situation if we consider any point. the body or particle is moving with a velocity
vector v. so we can say as the particle is moving in a curve, it’s direction is changing. It may be possible that its magnitude also
changes. And at this point, it is quite sure that velocity
direction is along the tangent of the curve, in which it is moving. That is the trajectory of its motion. Say at this point, a force f is applied to
this particle at an angle theta, to the direction of its motion. That is, angle from the tangent of this particle
at, this, point of the curve. Now, if we talk about a force this force will
have 2 components, one is along the tangent. this will be f-coz-theta. Other component of this force will be along
the normal to the curve, that is trajectory of motion, it is f-sine-theta. Here you can see. a component of force f-coz-theta is acting
along the direction of velocity and f-sine-theta is acting perpendicular to the direction of
velocity. So in this situation we can write, the force
f-coz-theta which is acting along the direction of velocity is responsible. For change in magnitude of. Velocity vector. And f-sine-theta the force which is acting
perpendicular to velocity is, responsible for, change in direction of v-vector. This is the way how we analyze this. Whenever a particle moves, a force acts on
it. We can directly state. The component of force which is acting along
velocity will change the magnitude of velocity, and the component which is acting perpendicular
or normal to velocity will change, the direction of velocity.