Question

A cord is wound around the circumference of a wheel of radius 15 cm . The axis of wheel is horizontal. A mass of 0.5 kg is attached at the end of the chord and it is allowed to fall from rest. If the weight falls 1.5 metre in 4 seconds. What is the angular acceleration of the wheel? Also calculate the moment of inertia of the flywheel.

Answer 1

Dear Student,
now as given

the distance moved by the wheel = 1.5 m

in time = 4 s

so, the linear velocity will be

v = 1.5m /4s

or

v = 0.375 m/s

now,

the angular velocity will be

w = v/r

here r = 0.15 m

or

w = 0.375 / 0.15

thus,

w = 2.5 rad/s

so,

the angular acceleration of the wheel will be

a = w/t = 2.5 / 4

or

a = 0.625 rad/s²

and

the moment of inertia will be

I = T/a

here

torque T = r x F = r x mg

or

T = 0.15 x (0.5x9.8)

so,

T = 0.735 Nm

and

so,

I = 0.735/0.625

thus, moment of inertia

I = 1.176 kg.m²
Regards