CdiculalPeriodic Table Question 8 of 10 Sapling Learning Map A horizontal circul

Question

CdiculalPeriodic Table Question 8 of 10 Sapling Learning Map A horizontal circular platform rotates counterclockwise about its axis at the rate of 0.805 rad/s. You, with a mass of 71.7 kg, walk clockwise around the platform along its edge at the speed of 1.17 m/s with respect to the platform. Your 20.9-kg poodle also walks clockwise around the platform, but along a circle at half the latform's radius and at half your linear speed with respect to the platform. Your 17.3-kg mutt, on the other and, 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 90.1 kg and radius 1.89 m. Calculate the total angular momentum of the system. Number kg m/s

Explanation / Answer

Given

horizontal circular platform with radius r = 1.89m, mass M = 90.1 kg

rotating at the rate of W = 0.805 rad/s ,

mass of you m1 = 71.7 kg, speed v1 = 1.17m/s, at a distance r

mass of poodle m2 = 20.9 kg , speed v2 = v1/2 = 1.17/2 = 0.585 m/s at r2 = r/2 position

mass of mutt m3 = 17.3 kg, speed v3 = 0 m/s, at a position r3 = (3/4)(r) from center

we know that the anglular momentum L == I*W

where I is moment of inertia of disc I = 0.5*M*r^2 , W = 0.805 rad/s

and the relation between V and W is V = r*W,

angular speed of you is W1 = v1/r = 1.17/1.89 rad/s = 0.6190 rad/s

same way for poodle is W2 = v2/r2 = 0.585/0.945 rad/s = 0.6190 rad/s

and for mutt W3 = v3/r3 = 0 rad/s

moment of inertia of disk is I = 0.5*90.1*1.89^2 kg m^2 = 160.923105 kg m^2

  

as the disc rotating in anticlockwise direction then its angular momentum is positive and the remaining are in clockwise direction their angulat momeneta are negative

total angular momentum of the system is

L_T = L_disk+L_other

L_other = (m1*v1*r1)+(m2*v2*r2)+(m3*v3*r3)

= (71.7*1.17*1.89)+(20.9*0.585*0.945) +(17.3*0*3*1.89/4) kg m2/s

= 170.1042 kg m2/s

L_disc = I*W = 160.923105*0.805 kg m2/s

= 129.5431 kg m2/s

L_T = 129.543099525-170.1042 kg m2/s

L_T = -40.5611 kg m2/s

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