Question

A constant
force of 40N is
applied tangentally
to the rim of a wheel
with 20cm radius.
The wheel has a
moment of inertia
30kg.m2. Find
(a)angular
acceleration
(b)angular speed
after 4seconds from
rest (c)the number
of revolutions made
in that 4 seconds
(d)show that the
work done on the
wheel in this
4seconds=kinetic
energy of th wheel
after 4seconds

Answer 1

torque = moment of inertia * angular acceleration
40 * 0.20 = 30 alpha

alpha = .267 radians/sec^2

omega = alpha * t

omega= .267 * 4 = 1.07 radians/sec

angle = (1/2) alpha *t^2
= .5 *.267 *16 = 2.136 radians
divide by 2 pi = .34 revolutions
torque * angle = work in
= 8 * 8.53 = 17.1 Joules
(1/2)I omega^2 = Ke
= .5 * 30 * 1.07^2 = 17.1 Joules