Definition:
- Circular Motion: Movement of an object along a circular path.
- Uniform Circular Motion: Motion of an object traveling in a circle with a constant speed. While the speed (magnitude of velocity) remains constant, the direction of velocity continuously changes.
Examples of Circular Motion:
- An artificial satellite orbiting the Earth.
- A stone tied to a rope and swung in circles.
- A car turning through a curve on a race track.
- An electron moving perpendicular to a uniform magnetic field.
- A gear turning inside a mechanism.
Angular Displacement and Angular Velocity
Angular Displacement:
- The angle through which an object has rotated or moved around a circular path.
- It represents the distance an object moves along a circular path.
Angular Velocity:
- The rate at which angular displacement changes over time.
- It measures how quickly an object rotates around a circle.
Displacement:
- Linear Displacement: Distance from the initial to the final position along a straight line.
- Angular Displacement: Rotation of a body around a circular path.
Example:
- If a wheel rotates through an angle ΘThetaΘ, you can measure the rotation in different units:
- Revolutions: 1 revolution = 360°
- Degrees: 180° corresponds to ½ revolution
- Radians: 1 revolution=2π radians1
Relationship: Θ=S/R
- Where:
- ΘThetaΘ = Angular displacement (in radians)
- S = Arc length (distance traveled along the circle)
- R = Radius of the circle
Tangential Velocity and Angular Velocity
Tangential Velocity (Linear Velocity):
- Velocity of an object moving along the circular path. It is tangent to the circle at the object’s location.
- Formula: v=S/t where S is the arc length and t is time.
Angular Velocity:
- Relation to Tangential Velocity: v=ω×R
- Where:
- v = Tangential velocity
- ωomega = Angular velocity (in radians per second)
- R = Radius of the circle
- Note: In uniform circular motion, speed is constant, but the direction of the velocity vector changes continuously, leading to a changing velocity.