Explanation:
Given that,
Force,
Position of the particle,
(a) The toque on a particle about the origin is given by :
Taking the cross product of above two vectors, we get the value of torque as :
(b) Let is the angle between r and F. The angle between two vectors is given by :
Answer:
It is to reduce the expected relative error of the measurement.
Explanation:
If there was a way to measure without error, this method would be unnecessary. In practice, the pesky error is always there. The sources are varied: inexact instrument, small inaccuracies in starting/stopping the timer, etc. But, it is reasonable to assume that such an error is random and has an expected spread that is <em>independent</em> of the actual duration of measurement. Under such assumptions, the methods offers a great advantage:
Let ε denote an additive measurement error. Let the error be random, symmetric (negative/positive), distributed in some fixed range independent of the actual measured value. The error represents an additive component in our measurement, i.e., (measurement) = (true value) + (error). In the case of one period T, we get to measure the duration T':
so the relative error is
In a separate experiment, suppose you measure n periods. Same error applies:
we can get a single period by dividing the measured value by n:
and the relative error of such a result will be:
which is n times smaller than the relative error of the single measurement above. The more periods are included in the measurement, the smaller the expected error!