Obtain formula of linear speed of an object performing uniform circular motion along a circular path of radius r. show that it performs accelerated motion
Answers
Angular Displacement
The angle which is subtended by the position vector at the center of the circular path refers to the angular displacement.
Angular Displacement (Δθ) = (ΔS/r)
Where Δ’s refers to the linear displacement while r is the radius. Radian is the unit of Angular Displacement.
Angular Acceleration
It refers to the rate of time of change of angular velocity (dῶ).
Angular acceleration (α) = dῶ/dt = d2θ / dt2
Its unit is rad/s2 and dimensional formula [T]-2. The relation between linear acceleration (a) and angular acceleration (α)
A = rα, where r is the radius.
Angular Velocity
It refers to the time rate change of angular displacement (dῶ).
Angular Velocity (ῶ) = Δθ/Δt
Angular Velocity is a vector quantity. Its unit is rad/s. The relation between the linear velocity (v) and angular velocity (ῶ) is
v = rῶ
Centripetal Acceleration
It refers to an acceleration that acts on the body in circular motion whose direction is always towards the center of the path.
Centripetal Acceleration (α) = v2/r = rῶ2.
Hello
As acceleration is the ratio of the change in velocity over time. Therefore, acceleration also points towards the centre of the circle. Further, as the body moves in the circle