Question

A horizontal circular platform rotates counterclockwise about its axis at the rate of 0.841 rad/s.0.841 rad/s. You, with a mass of 72.1 kg,72.1 kg, walk clockwise around the platform along its edge at the speed of 1.17 m/s1.17 m/s with respect to the platform. Your 20.3 kg20.3 kg poodle also walks clockwise around the platform, but along a circle at half the platform's radius and at half your linear speed with respect to the platform. Your 18.5 kg18.5 kg mutt, on the other hand, sits still on the platform at a position that is 3/4 of the platform's radius from the center. Model the platform as a uniform disk with mass 92.5 kg92.5 kg and radius 1.87 m.1.87 m. Calculate the total angular momentum of the system.

Answer 1

Answer:

The total angular momentum of the system is $217.46\ kg-m^2/s$.

Explanation:

Given that,

Angular speed = 0.841 rad/s

Mass of platform = 72.1 kg

Speed = 1.17 m/s

Mass of poodle = 20.3 kg

Mass of mutt = 18.5 kg

Distance =3/4 of the platform's radius from the center

Mass of disk = 92.5 kg

radius = 1.87 m

Angular momentum is the product of moment of inertia and angular speed.

We need to calculate the angular momentum of person

$L_{person} = I\omega$

$L_{person}=\dfrac{1}{2}mr^2\times\omega$

$L_{person}=\dfrac{1}{2}\times72.1\times(\dfrac{v}{\omega})^2\times\omega$

$L_{person}=\dfrac{1}{2}\times72.1\times(\dfrac{1.17}{0.841})^2\times0.841$

$L_{person}=58.679\ kg m^2/s$

We need to calculate the angular momentum of platform

$L_{platform}=\dfrac{1}{2}mr^2\times\omega$

Put the value into the formula

$L_{platform}=\dfrac{1}{2}\times92.5\times1.87^2\times0.841$

$L_{platform}=136.02\ kg m^2/s$

We need to calculate the angular momentum of poodle

$L_{poodle}=\dfrac{1}{2}mr^2\times\omega$

Put the value into the formula

$L_{poodle}=\dfrac{1}{2}\times20.3\times(\dfrac{1.87}{2})^2\times0.841$

$L_{poodle}=7.4625\ kg m^2/s$

We need to calculate the angular momentum of mutt

$L_{mutt}=\dfrac{1}{2}mr^2\times\omega$

$L_{mutt}=\dfrac{1}{2}\times18.5\times(\dfrac{3}{4}\times1.87)^2\times0.841$

$L_{mutt}=15.302\ kg m^2/s$

We need to calculate the total angular momentum

$L=L_{person}+L_{platform}+L_{poodle}+L_{mutt}$

$L=58.679+136.02+7.4625+15.302$

$L=217.46\ kg-m^2/s$

Hence, The total angular momentum of the system is $217.46\ kg-m^2/s$.