System of Particles and Rotational Motion

A rigid body can undergo pure

A rigid body can undergo pure translation (all particles have same velocity), pure rotation (particles move in circles about a fixed axis), or a combi

The point where the total mass

The point where the total mass of a system can be considered concentrated. For n particles: R = (Σmᵢrᵢ)/M, where M is total mass. The CM moves as if a

Angular velocity ω = dθ/dt measures

Angular velocity ω = dθ/dt measures how fast an object rotates, while angular acceleration α = dω/dt measures the rate of change of angular velocity.

For vectors a and b

For vectors a and b: a × b has magnitude |a||b|sinθ and direction given by right-hand rule. Essential for defining torque (τ = r × F) and angular mome

The rotational equivalent of force

The rotational equivalent of force, τ = r × F. Magnitude is τ = rFsinθ = r⊥F = rF⊥. Torque causes angular acceleration according to τ = Iα (rotational