In circular motion, velocity, acceleration, and displacement are all related to the properties of the circular path and the time taken to travel along that path. Here's how you can find these quantities:
- Velocity: Velocity in circular motion refers to the rate of change of displacement with respect to time. It is a vector quantity that has both magnitude and direction.
In uniform circular motion (when the object moves at a constant speed along a circular path), the magnitude of the velocity remains constant, but its direction changes continuously.
The formula for velocity in circular motion is:
v = rω,
where v is the magnitude of the velocity, r is the radius of the circular path, and ω (omega) is the angular velocity (measured in radians per unit time).
- Acceleration: Acceleration in circular motion refers to the rate of change of velocity with respect to time. It is also a vector quantity.
In uniform circular motion, the object undergoes centripetal acceleration directed towards the center of the circle. The centripetal acceleration keeps the object moving in a circular path.
The formula for centripetal acceleration is:
a = rω²,
where a is the magnitude of the acceleration, r is the radius of the circular path, and ω (omega) is the angular velocity.
- Displacement: Displacement in circular motion refers to the change in position of an object as it moves along the circular path. It is a vector quantity and is generally measured in terms of angle or arc length.
The displacement in circular motion is typically represented as θ (theta), which is the angular displacement. It is measured in radians and represents the angle through which an object has moved along the circular path.
The formula for angular displacement is:
θ = ωt,
where θ is the angular displacement, ω (omega) is the angular velocity, and t is the time taken.
To convert angular displacement (θ) to linear displacement (s) along the circumference of the circle, you can use the formula:
s = rθ,
where s is the linear displacement and r is the radius of the circular path.
It's important to note that these formulas apply to uniform circular motion, where the speed remains constant. In cases of non-uniform circular motion or situations with changing speeds, additional factors may need to be considered.