Uniform circular motion occurs when an object moves along a circular path with a constant speed. Despite the speed remaining unchanged, the direction of motion continuously changes, which means the velocity (a vector quantity) is not constant. This change in direction necessitates the presence of acceleration, known as centripetal acceleration.
Key Features of Uniform Circular Motion
1.Constant Speed:
In this magnitude of the velocity remains the same throughout the motion.
And the object covers equal distances along the circular path in equal time intervals.
2. Variable Velocity:
Of course, velocity is a vector quantity (having both magnitude and direction) and in this the direction changes continuously and velocity varies.
3. Acceleration:
In this the change in velocity is caused by centripetal (Centripetal is the force that acts on an object moving in a circular path, directed towards the center of the circle. It is responsible for keeping the object in circular motion by continuously changing the direction of its velocity.) acceleration, directed towards the center of the circular path.
And acceleration is necessary to keep the object should move in a circular path.
4. Force:
In this centripetal force acts on the object, directed towards the center of the circle. This force is responsible for the centripetal acceleration.
Examples include gravitational force (in planetary motion), tension in a string (when a stone is tied and rotated), or friction (in a car turning on a circular track).
Kinematic Quantities in Uniform Circular Motion
1.Angular Displacement (θ):
In angular displacement angle subtended by the radius of the circle at the center when object moves.
It is measured in radians (rad) or degrees.
2. Angular Velocity (ω):
It is stated as rate of change of angular displacement.
Formula: ω = θ / t, where t is time.
SI Unit is radians per second (rad / s).
3. Linear Velocity (v):
Linear velocity is the speed of the object along the circular path.
It is related to angular velocity as v = rω, where r is the radius of the circle.
SI Unit is meters per second (m/s).
4. Centripetal Acceleration (ac):
Centripetal acceleration is stated that it is directed towards the center of the circle.
Formula: ac = v2 / r = ω2r
5. Time Period (T)
Time period is time taken by the object to complete one full revolution.
Formula: T=2πr / v = 2π / ω.
6. Frequency (f)
Frequency is the number of revolutions per second.
It is related to the time period as f = 1 / T
SI Unit is Hertz (Hz).
Equations of Motion in Uniform Circular Motion
Equations of motion for straight-line motion is linear quantities, where as uniform circular motion apply angular quantities. These are analogous:
Angular displacement: θ = ωt.
Relationship between linear and angular quantities:
v = rω.
Examples of Uniform Circular Motion
1. Earth’s Revolution Around the Sun:
The Earth moves in an almost circular orbit around the Sun at a nearly constant speed.
The gravitational force acts as the centripetal force.
2. A Satellite Orbiting a Planet:
Satellites maintain a circular orbit due to the gravitational pull of the planet.
3. A Car Turning on a Circular Track:Friction between the tires and the road provides the necessary centripetal force.
4. A Stone Tied to a String
When whirled in a circular path, the tension in the string acts as the centripetal force.
Important Points to Remember
1. Velocity is vector quantity always tangent to the circular path.
2. Centripetal force does not do any work because it acts perpendicular to the velocity of the object.
3. Due to absence of centripetal force in the object is moving tangentially to the circular path (Newton’s First Law of Motion states).
4. Ft = 0; Fnet = Fc = mv2 / r = mω2 r
5. Fc = mv2 / r, since the speed v is constant, the magnitude of centripetal force Fc is always perpendicular to velocity. So that the direction Fc must change. In other words Fc is always variable force.
6. Work done by Fc is always zero.
7. Because, centripetal force can not change the kinetic energy of a particle. It provides acceleration but does not work.
8. Power = Fc .v = 0
Applications of Uniform Circular Motion
1.Artificial Satellites:
Circular motion helps in designing the satellite orbits for calculating their speed and time period.
2. Amusement Park Rides:
In the rides like Ferris wheels and merry-go-rounds utilise principles of circular motion.
3.Engineering:
When curved roads and racetracks are being designed/ constructed then it is kept in mind about the centripetal force requirements.
Note
Uniform circular motion is utitise to understand the dynamics of objects in circular paths. It is constant speed and a continuously changing direction of velocity in the presence of centripetal acceleration and force. The concepts of angular displacement, velocity, and acceleration form the backbone of circular motion for analysing .
Uniform circular motion is the motion of an object moving in a circular path with a constant speed. Despite the speed being constant, the velocity changes due to the continuous change in the direction of motion.
No, the velocity is not constant because velocity is a vector quantity, and its direction changes continuously in circular motion, even though the speed (magnitude of velocity) remains constant.
Centripetal acceleration is the acceleration which direct towards the center of the circular path. It is required for continuously changing the direction of the object’s velocity to ensure the object should remains in the circular path.
Source of centripetal force depends on the situation:
Gravity in planetary orbits.
Friction for a car turning on a curved road.
Tension in the string for a whirling object.
The relationship is given by v = rω, where:
v is the linear velocity,
r is the radius of the circular path,
ω is the angular velocity.
No, centripetal force does not work because it acts perpendicular to the direction of the object’s displacement at every point of the motion.
In uniform circular motion, the speed of the object remains constant.
In non-uniform circular motion, the speed of the object varies when it moves along the circular path.
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