Question

A gramophone disc rotates at 60 rpm. A coin of mass 18 g is placed at a distance of 8cm from the center. Calculate the centrifugal force on the coin.

Answer 1

In this question, we calculate the centrifugal force. Centrifugal force is an apparent force felt by the body moving along a curved and circular path, acting in the outward direction. It is also a fictitious force, and this force arises only when the system is not about the frame of reference.

Complete step by step answer:
Given that,the gramophone disc is revolving with the angular velocity $\omega$at 60 rpm. We know that a force required to make a body move along a circular path with uniform speed is called centripetal force.
Centripetal force = mass centripetal$\times$acceleration.
$\therefore \;{\rm{F}}\;{\rm{ = mr}}{\omega ^2}$
F is the centripetal force, r is radius; m is mass and angular velocity.
Mass given (m) = $18g\; = \;0.018{\rm{kg}}$
Radius(r) = $8\;{\rm{cm}}\;{\rm{ = }}\;{\rm{0}}{\rm{.08m}}$
Now, the angular velocity $\omega \; = \,60rpm\, = \;\dfrac{{2\pi 60\;}}{{60}}rad/s = \;2\pi \;rad/s$
So we substitute the values in the above relation we get,
${\rm{F}}\;{\rm{ = }}0.018 \times 0.08 \times {(2 \times 3.14)^2}\;$
${\rm{F}}\;{\rm{ = }}0.018 \times 0.08 \times 4 \times 9.8596\; = 0.0568{\rm{N}}$

Hence the centrifugal force of the coin is 0.0568N.

Additional information: A phonograph, in its later forms, called a gramophone since the 1940s, called a record player, is a device for the mechanical recording and reproduction of sound.

Note: We find the value of the coin in the S.I unit system. Also, we calculate in the C.G.S system then the units become dyne. Here we also take the value of pi = 3.14; we use a different pi value if that is given in the question.