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 = ωr2dm L =

ωr2dm = ω r2dm

L = Iω

3

Newton’s 2nd Law L =

• i Li =
• i ri × pi

dL dt =

• i

    ri × dpi

dt + dri dt × pi

    

dL dt =

• i

    ri × dpi

dt + vi × mivi

    

dL dt =

• i ri × dpi

dt =

• i ri × Fi =
• i τ =

τext

dL dt =

τext

4

Conservation of Angular Momentum If

τext = dL

dt = 0,then L= a constant

Li = Lf For rigid bodies Iiωi = Ifωf

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? Iiωi = Ifωf ωf = Ii If ωi = mr2

i

mr2

f

ωi = r2

i

r2

f

ωi ωf = (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

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