Question

A 0.75-m-diameter solid sphere can be rotated about an axis through its center by a torque of 12.8 m∗N which accelerates it uniformly from rest through a total of 170 revolutions in 14.0 s .

What is the mass of the sphere?

Answer 1

here,

the diameter of solid sphere , d = 0.75 m

the radius of solid sphere , r = d/2

r = 0.375 m

the torque applied , T = 12.8 N.m

the time taken , t = 14 s

the angle covered , theta = 170 rev = 1067.6 rad

let the angular acceleration be alpha

theta = w0 * t + 0.5 * alpha * t^2

1067.6 = 0 + 0.5 * alpha * 14^2

solving for alpha

alpha = 10.89 rad/s^2

let the mass of sphere be m

the torque applied , T = I * alpha

12.8 = (0.4 * m * r^2) * ( 10.89)

12.8 = (0.4 * m * 0.375^2) * ( 10.89)

solving for m

m = 20.9 kg

the mass of sphere is 20.9 kg