   Chapter 8, Problem 74P

Chapter
Section
Textbook Problem

A particle of mass 0.400 kg is attached to the 100-cm mark of a meter stick of mass 0.100 kg. The meter sack rotates on a horizontal, frictionless table with an angular speed of 4.00 rad/s. Calculate the angular momentum of the system when the stick is pivoted about an axis (a) perpendicular to the table through the 50.0cm mark and (b) perpendicular to the table through the 0-cm mark.

(a)

To determine
The angular momentum of the system when the stick is pivoted about an axis perpendicular to the table through the 50.0cm mark.

Explanation

The angular momentum of the system is defined as L=Isysω=(Istick+Iparticle)ω and the moment of inertia of meter stick and the mass are Istick=mL2/12 and Iparticle=M(LL/2)2 . Using these expressions in the expression of angular momentum of the system, the value of angular momentum is calculated.

Given info: Mass of the particle is 0.100kg , mass of meter stick is 0.400kg , length of the meter stick is 100cm , and angular speed of the system is 4.00rad/s .

The formula for the angular momentum of the system is,

L=(m12+M4)L2ω

• m is mass of the stick.
• M is mass of the particle.
• L is length of the stick.
• ω is angular speed of the system.

Substitute 0.100kg for m , 0

(b)

To determine
The angular momentum of the system when the stick is pivoted about an axis perpendicular to the table through the 0.00cm mark.

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