Question

A child\'s top is held in place, upright on a frictionless surface. The axle has a radius of r = 2.96 mm. Two strings are wrapped around the axle, and the top is set spinning by applying T = 2.40 N of constant tension to each string. If it takes 0.740 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.

Answer 1

Answer:

Explanation:

Given

radius r=2.96 mm

Tension T=2.4 N

time taken=0.74 s

Let $\alpha$be the angular acceleration

$2 T\times r=I\times \alpha$

$2\times 2.4\times 2.96\times 10^{-3}=0.5\times m\times (2.96\times 10^{-3})^2\times \alpha$

$\alpha =\frac{4\times 2.4}{m\times 2.96\times 10^{-3}}$

$\alpha =\frac{3.24\times 10^3}{m} rad/s^2$

$\omega =\omega _0+\alpha \cdot t$

$\omega =0+\frac{3.24\times 10^3}{m}\times 0.74$

$\omega =\frac{2.4\times 10^3}{m} rad/s$

Angular momentum

$L=I\omega$

$L=0.5\times mr^2\times \omega$

$L=0.5\times m\times (2.96\times 10^{-3})^2\times \frac{2.4\times 10^3}{m}$

$L=0.01051 kg-m^2/s$