Question

A nonuniform cylinder (radius = 0.14 m, center-of-mass rotational inertia = 2.22×10-2 kg·m2, mass = 1.33 kg) starts from rest and rolls without slipping down a plane with an angle of inclination of 24.2°. How long does it take to travel 1.56 m along the incline?

Answer 1

Here ,

moment of inetia , I = 2.22 *10^-2 kg.m^2

mass , m = 1.33 Kg

radius , r = 0.14 m

theta = 24.2 degree

let the acceleration of the cycliner is a

a = net force/effective mass

a = (m * g * sin(theta))/( m + Icom/R^2)

a = (1.33 * 9.8 * sin(24.2))/(1.33 + (2.22 *10^-2/.14^2) )

a = 2.17 m/s^2

distance , d = 1.56 m

let the time taken is t

Using second equation of motion

d = u * t + 0.5 * at^2

1.56= 0.5 * 2.17 * t^2

t = 1.20 s

the time taken to travel is 1.56 m is 1.20 s

I hope help you !!