|Table of contents|
|Difference between Uniform Linear Motion and Uniform Circular Motion|
|Angular Displacement and Angular Velocity|
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.
(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.
- Option A is incorrect because a car moving along a straight road does not follow a circular path.
- Option B is incorrect because a cyclist pedaling up a hill experiences varying speeds, not uniform circular motion.
- Option D is incorrect because a person walking in a straight line does not follow a circular path.
- Option C is the correct answer because a satellite orbiting around the Earth at a fixed distance follows a circular path and covers equal distances along the circumference in equal intervals of time.
- In uniform circular motion, the speed remains constant, but the direction of velocity changes continuously.
- Therefore, a satellite orbiting around the Earth is an example of uniform circular motion.
Uniform linear motion
Uniform circular motion
The direction of motion does not change.
The direction of motion changes
The motion is non-accelerated
The motion is accelerated
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.
If ∠ACB = θ radians
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.
2π radians = 360°
1 radian = 57.30
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
Unit Angular displacement = θ (in radian)
Angular velocity ω
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.
- In this type of motion, the direction of motion continuously changes as the object moves along the circular path.
- The motion is considered to be accelerated because even though the speed remains constant, the object is constantly changing its direction.
- The angle covered by a body in 1 second is called angular velocity, which is a measure of how quickly the object is rotating.
- The trajectory of a projectile, on the other hand, refers to the path followed by an object that is launched into the air and subject to the force of gravity. It is typically parabolic in shape.
- Therefore, the correct statement about Uniform Circular Motion is that the angle covered by a body in 1 second is called angular velocity (Option C).
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
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
This equation shows that the height H is maximum when 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
For maximum range sin 2θ = 1 or 2θ = 90° or θ = 45°
and the maximum range,
Obviously the maximum range is achieved when angle of projection is 45°.
|1. What is circular motion?|
|2. What is the difference between uniform linear motion and uniform circular motion?|
|3. What is a radian?|
|4. What is angular displacement and angular velocity?|
|5. What are some real-life examples of uniform circular motion?|