A person of mass 55 kg stands at the center of a rotating merry-go-round platfor
ID: 1585857 • Letter: A
Question
A person of mass 55 kg stands at the center of a rotating merry-go-round platform of radius 3.3 m and moment of inertia 670 kg · m2. The platform rotates without friction with angular velocity 1.5 rad/s. The person walks radially to the edge of the platform.
(a) Calculate the angular velocity when the person reaches the edge.
rad/s
(b) Calculate the rotational kinetic energy of the system of platform plus person before the person's walk.
J
(c) Calculate the rotational kinetic energy of the system of platform plus person after the person's walk. (Note that each step represents a completely inelastic collision, implying that some kinetic energy is lost as heat.)
J
Explanation / Answer
mass of the person, m1=55 kg
radius, r=3.3 m
moment of Inertia, I=670 kg/m^2
w1=1.5 rad/sec
a)
use,
L_initial= L_final
I1*w1=(I1+I2)*w2
670*1.5=(I1+m1*r^2)*w2
670*1.5=(670+55*3.3^2)*w2
===> w2=0.792 rad/sec
b)
K.E_initial=1/2*I1*W1^2
=1/2*670*1.5^2
=753.75 J
c)
K.E_final=1/2*(I1+I2)*w2^2
=1/2*(670+55*3.3^2)*0.792^2
=397.98 J
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.