In a garden a boy is swinging in the standing position how will the time period of the swing be affected if the boy sites down on the swing?
Time period will increase
During this swinging, angular momentum of the whole system will be constant.
So,angular momentum =
Now,when the boy sits down,moment of inertia increases,well that's because,here we calculate the moment of inertia along that axis,from where the swing is swinging to and fro.
So,initially,his head was closer to the point of swing than his legs,so his body mass was distributed along the radius,but on sitting,the whole mass went towards the cicumferance,so
Now,as angular momentum is conserved,so on increasing
The boy sitting down will make the time period increase unless he is really, really tall!
To understand this problem, we will make a few semi-realistic assumptions. We will model the boy standing straight on the swing by a straight uniform rod of mass
Let us denote the height of the boy and the length of the swing by
For a compound pendulum of moment of inertia
for small oscillations. So, the time period is given by
For the boy standing up, his center of gravity is at a distance
On the other hand, for the boy sitting down, the moment of inertia is
Sitting down will increase the time period,
Thus the boy sitting down will make the time period increase unless he is really, really tall!