Rotational Dynamics — Important Questions

Constant speed, Acceleration directed towards center, Periodic motion

In UCM, speed is constant but velocity changes direction continuously. Centripetal acceleration is always directed towards center. The motion repeats in equal intervals of time.

Mass of the object, Distribution of mass, Axis of rotation

Moment of inertia depends on mass, how that mass is distributed relative to the axis, and the position of the axis. Angular velocity and material properties don't affect I directly.

π s

For conical pendulum, T = 2π√(L cos θ/g) = 2π√(1 × cos 60°/10) = 2π√(1 × 0.5/10) = 2π√(0.05) = 2π × √(1/20) = 2π/√20 = 2π/(2√5) = π/√5 ≈ π s

√(rg)

At the topmost point, for minimum speed, tension becomes zero. So mg = mv²/r, which gives v = √(rg)