Angular Momentum Angular Momentum Newtons Second Law Conservation - PDF document

Angular Momentum • Angular Momentum • Newton’s Second Law • Conservation of Angular Momentum • Homework 1

Angular Momentum of a Particle L = r × p L = rmv sin φ 2

Angular Momentum of a Rigid Body dL = rvdm = ωr 2 dm � ωr 2 dm = ω � r 2 dm L = L = Iω 3

Newton’s 2nd Law L = i L i = i r i × p i � � d L  r i × d p i dt + d r i   dt = dt × p i   �     i  d L  r i × d p i   dt = dt + v i × m i v i   �     i  d L i r i × d p i � τ ext dt = dt = i r i × F i = i τ = � � � d L � τ ext dt = 4

Conservation of Angular Momentum � τ ext = d L dt = 0 , then L = a constant If L i = L f For rigid bodies I i ω i = I f ω f 5

Example A child whirls a ball of mass m in a horizontal circle of radius 1.3 m at an angular speed of 35 rev/min. The child pulls in the cord, shortening the radius to 0.85 m. What is the new angular speed? 6

Example Solution A child whirls a ball of mass m in a horizontal circle of radius 1.3 m at an angular speed of 35 rev/min. The child pulls in the cord, shortening the radius to 0.85 m. What is the new angular speed? I i ω i = I f ω f ω i = mr 2 ω i = r 2 ω f = I i i i ω i mr 2 r 2 I f f f ω f = (1 . 3 m ) 2 (0 . 85 m ) 2 (35 rev/min ) = 82 rev/min 7

Homework Set 21 - Due Wed. Nov. 3 • Read Sections 10.8 & 10.9 • Answer Question 10.11 • Do Problems 10.39, 10.42, 10.44 & 10.45 8