A horizontal circular platform rotates counterclockwise about its axis at the ra

Question

A horizontal circular platform rotates counterclockwise about its axis at the rate of 0.965 rad/s. You. with a mass of 65.7 kg. walk clockwise around the platform along its edge at the speed of 1.09 m/s with respect to the platform. Your 20.3-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-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 90.9 kg and radius 1.89 m. Calculate the total angular momentum of the system.

Explanation / Answer

Your angular velocity:
_y = 0.965rad/s - 1.09m/s / 1.89m = 0.388 rad/s (cw)
poodle's angular velocity:
_p = 0.965rad/s - (1.09m/s / 2) / (1.89m / 2) = 0.388 rad/s (cw)

your I_y = mr² = 65.7kg * (1.89m)² = 234.69 kg·m²
poodle's I_p = 20.3kg * (1.89m / 2)² = 18.1 kg·m²
mutt's I_m = 18.5kg * (3 * 1.89m / 4)² = 37.17 kg·m²
disk I_d = ½mr² = ½ * 90.9kg * (1.89m)² = 162.35 kg·m²

total L = (I_d + I_m) + I_y * _y + I_p * _p
L = (162.35 + 37.17)kg·m² * 0.965rad/s - 234.69kg·m² * 0.388rad/s
- 18.1kg·m² * 0.388rad/s
L = 94.45 kg·m²/s (cw)

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