Question

A child's top is held in place upright on a frictionless surface. The axle has a radius of r=3.46 mm.r=3.46 mm. Two strings are wrapped around the axle, and the top is set spinning by applying T=2.65 NT=2.65 N of constant tension to each string. If it takes 0.590 s0.590 s for the string to unwind, how much angular momentum LL does the top acquire? Assume that the strings do not slip as the tension is applied.

Answer 1

5.22e-3 kg·m²/s

Step-by-step explanation:

Given

r = 3.46mm = 0.00346m

T = 2.90 N

time = 0.260s

By applying the torque

τ = F • r = 2 ×2.9N ×0.00346m

= 0.020 N·m

But τ = dL/dt,

dL is the change in angular momentum since Li = 0, Lf = dL.

hence,

dL = τ dt = 0.020N·m ×0.260s

= 0.0052kg·m²/s

= 5.22e-3 kg·m²/s