Uniform Circular Motion Class 9 Notes | EduRev

Science Class 9

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Class 9 : Uniform Circular Motion Class 9 Notes | EduRev

The document Uniform Circular Motion Class 9 Notes | EduRev is a part of the Class 9 Course Science Class 9.
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Circular motion
Motion of a particle (small body)along a circle (circular path), is called circular motion.
If the body covers equal distances along the circumference of the circle, in equal intervals of time, then motion is said to be a uniform circular motion. When a body moves along a circular path, then its direction of motion changes continuously. 

Note: A uniform circular motion is a motion in which speed remain constant but direction of velocity changes continuously.

Uniform Circular Motion Class 9 Notes | EduRev

Uniform Circular Motion Class 9 Notes | EduRev

 

Uniform Circular Motion Class 9 Notes | EduRev

Uniform Circular Motion Class 9 Notes | EduRev

Examples of uniform circular motion are:
(i) Motion of moon around the earth.
(ii) Motion of a satellite around its planet.
(iii) Motion of earth around the sun.
(iv) An athlete running on a circular track with constant speed.
(v) Motion of tips of the second hand, minute hand and hour hand of a wrist watch.

  • Circular motion is an accelerated motion. 
  • In a circular motion, velocity changes in direction only, the motion is said to be accelerated. 
  • Uniform linear motion is not accelerated but uniform circular motion is accelerated.

Difference between a uniform linear motion and a uniform circular motion. 

Uniform linear motion

Uniform circular motion

The direction of motion does not change.

The direction of motion changes
 continuously

The motion is non-accelerated

The motion is accelerated

RADIAN
It is a convenient unit for measuring angles in physics.
The arc AB of the circle, has length l and subtends an angle q at the centre C.

Uniform Circular Motion Class 9 Notes | EduRev

If  ∠ACB = θ radians

Uniform Circular Motion Class 9 Notes | EduRev

One radian is defined as the angle subtended at the centre of the circle by an arc which is equal in length to its radius.
Angle subtended by the circumference at the centre.

Uniform Circular Motion Class 9 Notes | EduRev

2π radians = 360°

Uniform Circular Motion Class 9 Notes | EduRev

1 radian = 57.30

Angular displacement and angular velocity :

Uniform Circular Motion Class 9 Notes | EduRev

The angle covered by a body in 1 sec. is called angular velocity.
It is usually denoted by w and measured in radian per sec.
If q is the angle covered in time 't' then :
Angular velocity =  Angular displacement \ time taken

Uniform Circular Motion Class 9 Notes | EduRev

Unit Angular displacement = θ (in radian)

Angular velocity ω

Uniform Circular Motion Class 9 Notes | EduRev

Relation between linear velocity and angular velocity.

Uniform Circular Motion Class 9 Notes | EduRev

Uniform Circular Motion Class 9 Notes | EduRev

 

Higher order thinking skill
Projectile's Motion
A projectile is an object moving in space (or air) under the effect of gravitational effect of earth alone (without any other external force) is called the projectile motion and the object is caled the projectile.
The examples of projectile are missile shot from a gun, a bomb released from an airplane, a batted cricket ball, a ball thrown at some angle with horizontal and a rocket after its fuel is exhausted.
The motion of a projectile may always be resolved into two perpendicular straight line motions, viz, horizontal and vertical motions. These motions in perpendicular directions are quite independent of each other.

 Path of Projectile :-

Consider a body is projected with velocity, making an angle θ, point of projection O as the origin the axis OX and OY being horizontal and vertical directions respectively. The initial velocity may be resolved into horizontal and vertical components.
Horizontal Component ux = u cosθ
Vertical Component uy = u sinθ

The trajectory of the projectile is parabolic.

Time of flight T :-
The time in which the porjectile again meets the horizontal plane is called the time of flight. The net vertical displacement of projectile in time of flight is zero (i.e. y = 0) ; therefore, time of flight (T) of projectile from

Uniform Circular Motion Class 9 Notes | EduRev

Maximum height H :-

At maximum height vertical component of projectile's velocity is zero, i.e., vy = 0
from relation v2 = u2 + 2as, we have

Uniform Circular Motion Class 9 Notes | EduRev

This equation shows that the height H is maximum when Uniform Circular Motion Class 9 Notes | EduRev That is why the athlete in high jump tries to throw his body vertically upward.

Range of Projectile :-

The horizontal distance traversed by the projectile in time of flight T is called the range of projectile.
∴ Range R = horizontal speed × time of flight = ux T

Uniform Circular Motion Class 9 Notes | EduRevUniform Circular Motion Class 9 Notes | EduRev

For maximum range sin 2θ = 1 or 2θ = 90° or θ = 45°
 and the maximum range, Uniform Circular Motion Class 9 Notes | EduRev

Obviously the maximum range is achieved when angle of projection is 45°.

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