Two uniform solid spheres have the same mass, 1.45 kg, but one has radius of 0.2
ID: 1552691 • Letter: T
Question
Two uniform solid spheres have the same mass, 1.45 kg, but one has radius of 0.276 m whale the other has a radius of 0.014 m. For each of the spheres, find the torque required to the sphere from rest to an angular velocity of 367 rad/s in 15.5 s. Each sphere rotates about an axis through its center. Torque on sphere with the smaller radius. Torque on sphere with the larger radius. For each sphere, what force applied tangentially at the equator would provide the needed torque? Force on sphere with the smaller radius. Force on sphere with the larger radius.Explanation / Answer
let
m1 = m2 = 1.45 kg
r1 = 0.276 m
m2 = 0.814 m
angular acceleration of the sphere, alfa = (w2 - w1)/t
= (367 - 0)/15.5
= 23.68 rad/s^2
1) Torque on sphere with the smaller radius, T1 = I1*alfa
= (2/5)*m1*r1^2*alfa
= (2/5)*1.45*0.276^2*23.68
= 1.046 N.m
2) Torque on sphere with the larger radius, T2 = I2*alfa
= (2/5)*m2*r2^2*alfa
= (2/5)*1.45*0.814^2*23.68
= 9.1 N.m
3) T1 = F1*r1
==> F1 = T1/r1
= 1.046/0.276
= 3.79 N
4) T2 = F2*r2
==> F2 = T2/r2
= 9.1/0.814
= 11.2 N
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