A child\'s top is held in place, upright on a frictionless surface. The axle has

Question

A child's top is held in place, upright on a frictionless surface. The axle has a radius of r = 4.21 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 0.800 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. Number kg middot m^2/s If the final tangential speed of point P, h = 33.0 mm above the ground, is 1.45 m/s and the angle theta is 17.0 degree, what is the top's moment of inertia? Number kg middot m^2

Explanation / Answer

angular momentum acquired, L = Torque*time

= 2*T*r*t

= 2*3.15*4.21*10^-3*0.8

= 0.0212 kg.m^2/s

from the figure, tan(theta) = R/h

R = h*tan(theta)

= 33*tan(17)

= 10.09 mm

= 0.01009 m

angular speed, w = v/R

= 1.45/0.01009

= 143.7 rad/s

now use, L = I*w

==> I =L/w

= 0.0212/143.7

= 1.48*10^-4 kg.m^2

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