Question

provides one model for solving this type of problem. Two wheels have the same mass and radius of 4.8 kg and 0.38 m, respectively. One has (a) the shape of a hoop and the other (b) the shape of a solid disk. The wheels start from rest and have a constant angular acceleration with respect to a rotational axis that is perpendicular to the plane of the wheel at its center. Each turns through an angle of 12 rad in 8.9 s. Find the net external torque that acts on each wheel.

Answer 1

here,

theta = 12 rad

t = 8.9 s

let the angular accelration be alpha

theta = 0 + 0.5 * alpha * t^2

12 = 0 + 0.5 * alpha * 8.9^2

solving for alpha

alpha = 0.303 rad/s^2

a)

for hoop

mass , m = 4.8 kg

radius , r = 0.38 m

the moment of inertia , I = m * r^2

I = 4.8 *0.38^2 kg.m^2 = 0.69 kg.m^2

the external torque , T = I * alpha

T = 0.69 * 0.303 N.m = 0.21 N.m

b)

for disk

mass , m = 4.8 kg

radius , r = 0.38 m

the moment of inertia , I = 0.5 * m * r^2

I = 0.5 * 4.8 *0.38^2 kg.m^2 = 0.345 kg.m^2

the external torque , T = I * alpha

T = 0.345 * 0.303 N.m = 0.104 N.m