Question

A solid wheel and a hollow cylinder each having equal mass and radius (20kg and 0.50 m) are set
into rotation by descending masses of 4.0kg . What is the angular acceleration of each object?

Answer 1

here,

mass , m = 20 kg

radius , r = 0.5 m

mass desending , M = 4 kg

moment of inertia of solid wheel , Is = 0.5 * m * r^2

Is = 0.5 * 20 * 0.5^2 kg.m^2 = 2.5 kg.m^2

the accelration , as = net force /effective mass

as = M * g /( M + Is/r^2)

as = 4 * 9.81 /( 4 + 2.5/0.5^2)

as = 2.8 m/s^2

the angular accelration , alphas = as /r

alphas = 2.8 /0.5 rad/s^2 = 5.6 rad/s^2

moment of inertia of hollow cyclinder , Ic = m * r^2

Ic = 20 * 0.5^2 kg.m^2 = 5 kg.m^2

the accelration , ac = net force /effective mass

ac = M * g /( M + Ic/r^2)

ac = 4 * 9.81 /( 4 + 5/0.5^2)

ac = 1.64 m/s^2

the angular accelration , alphac = ac /r

alphac = 1.64 /0.5 rad/s^2 = 3.27 rad/s^2