Uniform Cercular Motion

Key Notes :

Definition:

  • Uniform Circular Motion refers to the motion of an object that moves in a circular path with constant speed. The magnitude of the velocity remains the same, but the direction of the velocity is constantly changing.

Characteristics:

  • Constant Speed: The object moves at a constant speed, but its direction of motion changes continuously.
  • Centripetal Acceleration: Even though the speed is constant, the velocity is changing due to the continuous change in direction. This results in acceleration, called centripetal acceleration, which is always directed towards the center of the circle.
  • Centripetal Force: A force is required to keep the object moving in a circle. This force is called the centripetal force and is directed towards the center of the circle. It could be tension, gravitational force, or friction, depending on the scenario.

Formulae:

  • Centripetal Acceleration (aₐ):

aa = v2 / r

​where v is the speed of the object and r is the radius of the circular path.

  • Centripetal Force (Fₐ):

Fa = mv2 / r

where m is the mass of the object, v is its speed, and r is the radius of the circle.

Relationship Between Linear Velocity and Angular Velocity:

  • The object’s linear velocity v (speed along the path) is related to angular velocity ω (rate of change of angle) by:

v = ωr

where r is the radius of the circle and ω is the angular velocity in radians per second.

Period and Frequency:

  • Period (T): The time taken to complete one full revolution of the circle. It is related to the speed v and the radius r by the equation:

T = 2πr / v

  • Frequency (f): The number of revolutions per unit time. The relationship between period and frequency is given by:

f = 1 / T

Examples of Uniform Circular Motion:

  • A satellite orbiting the Earth.
  • A car moving around a circular track at constant speed.
  • The motion of an electron around the nucleus of an atom (idealized model).

Key Differences from Other Types of Motion:

  • Unlike linear motion, in uniform circular motion, the object’s velocity changes direction, even though its speed remains constant.
  • The object experiences a centripetal force that keeps it in the circular path, which is not present in linear motion.

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