The document discusses uniform circular motion and the position-velocity relation equation. It defines uniform circular motion as motion where the speed is constant but the direction is continuously changing, requiring a centripetal force. It provides the equation for the position-velocity relation as v^2 - u^2 = 2as. Finally, it gives examples of uniform circular motion like a stone on a string being rotated in a circle and the moon orbiting the Earth.

1. LEARNING OBJECTIVES-----VIDEO 3
•POSITION VELOCITY RELATION EQUATION –THIRD EQUATION OF
MOTION.
•UNIFORM CIRCULAR MOTION

2. 3.EQUATION FOR POSITION VELOCITY RELATION
As discussed ,distance travelled by a uniformly
Accelerated body in time t is given by area of
the space enclosed between velocity time graph
and time axis.
Distance travelled s=area of trapezium ODBE
=sum of parallel sides/2 * distance between
parallel sides
s=(OD+EB)/2 *OE
s=(u+v)/2 *t [v=u+at or v-u=at or t=v-u/a]
Putting value of t
s=(v+u)/2 *(v-u)/a
s=v2-u2/2a
v2-u2=2as position velocity relation

3. UNIFORM CIRCULAR MOTION
When a body travels equal distances in equal intervals of time ,over a circular
path, its speed is uniform.The motion of the body is said to be uniform circular
motion.The direction of the motion at any instant of time is along the tangent to
the circular path at that instant.

4. UNIFORM CIRCULAR MOTION (UCM)
In uniform circular motion,only speed
of the body is constant but direction of
motion of the body is changing
continuously .
Velocity of the body in UCM is
changing continuously .hence uniform
circular motion is an accelerated
motion.
but an external force is needed to move
a body uniformly in a circle which is
called centripetal force.

5. UNIFORM CIRCULAR MOTION
To calculate speed of body in
uniform circular motion –
r=radius of circular path
t=time taken to go once round
the circle
v=speed in uniform circular
motion
s=distance travelled in one
complete
revolution=circumference of
circle
s=2∏r speed=distance/time
v=2 ∏r/t

6. EXAMPLES OF UNIFORM CIRCULAR MOTION
A piece of stone tied to a thread and rotated in
a circle with uniform speed .
The necessary force F is provided by pull of
hand .When the stone is at A ,its speed is along
the tangent to the circle at A towards east.
When the stone is at B its speed is along the
tangent towards south.
If the thread breaks at B then the stone will fall
in south .

7. UNIFORM CIRCULAR MOTION
Moon moves around the earth uniformly in a circular orbit.
The necessary force is provided by gravitational pull of earth on the moon.

8. SUMMARY
• POSITION VELOCITY RELATION EQUATION –THIRD EQUATION
OF MOTION.
• UNIFORM CIRCULAR MOTION