Question

A wheel of diameter 3.0 cm has a 4.0-m cord wrapped around its periphery. Starting from rest, the wheel is given a constant angular acceleration of 2.0 rad/s^2. The cord will unwind in ?

Answer 1

circumference of wheel = \(\pi\)d =0.09m
No of turns of rope over the circumference = length / circumference ~ 44
The angle subtended by cord = 2\(\pi\) * no of turns = 88\(\pi\)
So, the wheel will have to rotate by 88\(\pi\) to unwind the entire rope.

There is a kinematical eqn for the rotational motion of the wheel.

\[\theta =\omega t+1/2\alpha \ t ^{2}\]

where \(\omega\) is the initial angular velocity of wheel
\(\alpha\) is the angular acceleration of the wheel.
\(\theta\) is the angle displacement of the wheel
t is the time of motion

Here \(\omega\)=0
\(\alpha\)=2
\(\theta\)=88\(\pi\)

Find t

Answer 2

then t will be ~16 !
Thanx :)

Answer 3

\[\theta=(lenght/radius) , so
\theta=(4/0.015) ~267\]

that a simple way to find \[\theta \]