Circular Motion

by
When an object travels around a circle or a circular path, is said to be in circular motion. Constant distance from a fixed point, called the circle’s center, characterises this motion. Item going in a circular course continuously changes direction, even if its speed remains constant.

Types of Circular Motion

1. Circular motion can be divided into two primary categories according to the object’s speed:
2. Uniform Circular Motion (UCM): Object traveling in a circular direction at a constant speed is said to be in uniform circular motion. Speed remains constant, the velocity varies as it encompasses both direction and speed. Velocity of a moving object varies continuously because its direction changes constantly.
3. Non-Uniform Circular Motion: Object’s speed changes along the circular path in non-uniform circular motion. This indicates that when an object moves, its velocity changes in both magnitude and direction.

Key Words

  • Angular Displacement (θ): This is the angle, expressed in radians (rad), that an object passes through on a circular path.
  • Angular Velocity (ω): In uniform circular motion, angular velocity remains constant and is defined as the rate at which the angular displacement changes with time. It is expressed in radians per second (rad/s).
  • Angular Acceleration (α): Angular acceleration, expressed in radians per second squared (rad/s2), is the rate at which angular velocity changes over time.
  • Centripetal Force (Fc): Force, which can be computed using the formula, is what maintains an object traveling on a circular route and always points in the direction of the circle’s center.
    Fc ​= mv2​ / r
    where m is the mass of the object,
    v is the linear velocity, and
    r is the radius of the circular path.
  • Centripetal Acceleration (ac): Acceleration, which is provided by, acts on an item traveling in a circle and in the direction of the center.
            Ac ​= v2​ / r  or  ac = ω2 r
  • Tangential Velocity (vt): At any given point, this is the linear velocity along the tangent to the circular path, and it may be linked to the angular velocity using the formula
             vt = ωr
Equations of Circular Motion
1. Relation between Linear and Angular Quantities:
S = rθ (Arc length, where s is the distance along the circle’s edge)
vt​ = ωr (Tangential velocity)
2. Centripetal Acceleration and Force:
ac = v2 / r ​= ω2r
Fc​ = mac​ = mv2​ / r
3. Frequency and Period of Circular Motion:
  • Frequency (f): The number of complete revolutions per unit time. Measured in hertz (Hz).
  • Period (T): The time taken for one complete revolution.
          T = 1 / f​
  • Relation to angular velocity:
             ω  = 2π f = 2π​ / T
1. Planets Orbiting the Sun: Gravitational force, the centripetal force, causes planets to orbit the sun in roughly round paths.
2. A Car Taking a Turn: Automobile travels in a curved path when it turns. Centripetal force required to maintain the car’s trajectory is generated by the friction between the tires and the road.
3. A Stone Tied to a String: Stone attached to a string swings in a circular motion. Centripetal force required for circular motion is produced by the tension in the string.
4. Rotating Amusement Park Rides: Circular motion is found in many amusement park attractions, where mechanical structures or a combination of forces create centripetal force.
 
Circular Motion -Car
Car
Note:-
Circular motion will help us better understand how forces and accelerations operate in different situations, whether it be with regard to the motion of heavenly bodies or common things. Anybody studying advanced physics needs to understand the fundamentals of circular motion, including centripetal force and acceleration, in order to understand more complex physical phenomena.
An object moving around a circle’s perimeter or along a circular path is said to be in circular motion. It is defined as moving a constant distance from a fixed central point while continuously changing direction.
There are two main types of circular motion:
  • Uniform Circular Motion (UCM): Object moves with a constant speed along a circular path, meaning the magnitude of velocity remains constant, but its direction changes continuously.
  • Non-Uniform Circular Motion: Object’s speed varies as it moves along the circular path, leading to changes in both the magnitude and direction of velocity.
Force that maintains an object traveling in a circle and always pointing in the direction of the circle’s center is known as centripetal force. It is required for circular motion because it supplies the inward force required to continuously alter the object’s velocity’s direction, guaranteeing that the object travels in a round path
Force that is applied to the circle’s center and is required for circular motion is known as the centripetal force. In other hand, centrifugal force is an imaginary or false force that, appears to act outward on an object moving in a circular direction. Because of inertia, it is regarded as an effect rather than a real force.
Friction supplies the required centripetal force in many circular motion scenarios, such as an automobile turning on a road, enabling the object to go in a round route. In the absence of adequate friction, the object’s inertia would cause it to continue moving in a straight line rather than along a curved path
Radians offer a straightforward link between the arc length and the circle radius, angular displacement is expressed in radians. Radian is a natural unit of measurement for rotational angles and a useful tool for streamlining the mathematics of circular motion.
No, a zero net force object cannot move in a uniform circular motion. It need a consistent centripetal force directed toward the circle’s center to produce uniform circular motion. According to Newton’s first law of motion, an object would move in a straight line if the net force was zero since there would be no force to modify the object’s direction of motion (inertia).

3 thoughts on “Circular Motion”

  1. Pingback: Potential Energy,Gravitational,Elastic,Electrostatic class11
  2. Pingback: Law of Conservation of Linear Momentum ,Isolated System ,
  3. Pingback: Centripetal Acceleration Class 11 important for students

Leave a comment