19 - 2D rigid body rotational kinetics - Angular momentum - 2D Rigid Body Rotational Kinetics Angular momentum Angular momentum L For a point

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2D Rigid Body Rotational Kinetics – Angular momentum Angular momentum L : – For a point mass (particle): L = m υ A = m υ r sin φ = m υ ┴ r A : perpendicular distance from O (pivot) to the line of υ G r : distance from O (pivot) to the point mass φ : angle between r and υ υ ┴ : velocity component perpendicular to r – For a rigid body in pure rotation: L = I ω about pivot point O – Direction of L : CW or CCW for 2D rotation Newton’s 2nd law for 2D rigid body pure rotation : dL dt τ Σ = Conservation of angular momentum Σ τ = 0 → L i = L f or L 1 = L 2 Note: Collision involving a pivoted rigid body: Conservation of momentum is NOT valid. Only conservation of angular momentum is applicable. Example 1. Two identical small spheres, each with mass 0.2 Kg, are mounted on a 0.8 Kg slender rod. The 0.9 m long slender rod pivoted at its center rotates in a horizontal plane, and the spheres can slide along the rod. The slender rod initially spins with an angular velocity of 30 rad/s when the spheres are 0.15 m from the center on each side.