Need help quickly! A child\'s top is held in place, upright on a frictionless su

Question

Need help quickly!

A child's top is held in place, upright on a frictionless surface. The axle has a radius of r= 2.46 mm. Two strings are wrapped around the axle, and the top is set spinning by applying T =3.15 N of constant tension to each string. If it takes 0.290 s for the string to unwind, how much angular momentum does the top acquire? Assume that the strings do not slip as the tension is applied. If the final tangential speed of point P, h = 31.0 mm above the ground, is 1.35 m/s and the angle 9 is 15.0 degree, what is the top's moment of inertia?

Explanation / Answer

couple acting on the top

M=T*2r

=0.0155 N-m

SO change in angular momentum

M*dt

=4.5*10^-3 kg.m^2/s

M=I*alpha

alpha=change in angular velocity/time

Now tantheta=R/h

R=8.30 mm

angular velocity=1.35/R

=162.65 rad/s

alpha=162.65/0.29

=560.86 rad/s^2

M=I*alpha

I=2.76*10^-5 kg-m^2 ans

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