Question

Two gerbils run in place with a linear speed of 0.50 m/s on an exercise wheel that is shaped like a hoop. Find the angular momentum of the system if each gerbil has a mass of 0.22 kg and the exercise wheel has a radius of 8 cm and a mass of 4.5 g.

Answer 1

Answer:

$L = 0.018 kg m^2/s$

Explanation:

Angular speed and linear speed is related to each other as

$v = R\omega$

here we know that

$v = 0.50 m/s$

$R = 0.08 m$

now we have

$\omega = \frac{v}{R}$

$\omega = \frac{0.50}{0.08}$

$\omega = 6.25 rad/s$

Now we know that moment of inertia of the system is given as

$I = (2M + m)R^2 [tex][tex]I = (2\times 0.22 + 0.0045)(0.08)^2$

$I = 2.84 \times 10^{-3} kg m^2$

Now angular momentum of the system is given as

$L = I\omega$

$L = (2.84 \times 10^{-3})(6.25)$

$L = 0.018 kg m^2/s$