Rotational Motion and Moment of Inertia

Flashcards covering key concepts from rotational motion: torque, moment of inertia, energy forms, angular momentum, rolling without slipping, and common shapes' I values.

What is the rotational form of Newton's second law?

Torque equals moment of inertia times angular acceleration: τ = I α.

How is torque defined for a force F applied at radius R?

Torque τ = F R (for tangential force).

Moment of inertia for a point mass m at distance R from rotation axis?

I = m R^2.

General definition of moment of inertia?

I = Σ mi ri^2 (sum over all mass elements).

Moment of inertia of a solid cylinder about its central axis?

I = (1/2) M R^2.

Moment of inertia of a hollow cylinder about its central axis?

I = M R^2 (thin-walled).

Moment of inertia of a uniform rod about its center?

I = (1/12) M L^2.

Moment of inertia of a uniform rod about one end?

I = (1/3) M L^2.

Moment of inertia of a solid sphere about its center?

I = (2/5) M R^2.

Moment of inertia of a hollow sphere about its center?

I = (2/3) M R^2.

Relation between linear and angular quantities for rolling without slipping?

v = ω R and a = α R.

Rotational kinetic energy?

K_rot = (1/2) I ω^2.

Translational kinetic energy?

K_trans = (1/2) m v^2.

Total mechanical energy in rotation problems?

E = PE + Ktrans + Krot.

Angular momentum of a rotating body?

L = I ω (for a rigid body); for a point mass, L = m v R.

Conservation of angular momentum?

If external torque is zero, Lbefore = Lafter.

Work done by torque on a rotating body?

W = ∫ τ dθ = τ Δθ (for constant torque).

Final speed for rolling without slipping down an incline?

v^2 = 2 g h / (1 + I/(m R^2)).