INTRODUCING 5 - days-a-week problem solving session for Math Olympiad and ISI Entrance. Learn More 

July 29, 2017

Button on a Rotating Platform

Try this beautiful problem, useful for Physics Olympiad, based on Button on a Rotating Platform.

The Problem:

A small button placed on a horizontal rotating platform with diameter (0.320m) will revolve with the plate when it is brought up to a speed of (40rev/min), provided the button is no more than (0.150m) from the axis. What is the coefficient of static friction between button and platform?

Discussion:

The button moves in a circle so it has acceleration (a_{rad}).
The coefficient of static friction $$ \mu_s=\frac{v^2}{Rg}$$ Expressing (v) in terms of the period (T), $$ v=\frac{2\pi R}{T}$$ so, $$\mu_s=\frac{4\pi^2R}{T^2g}$$.A platform speed of (40.0rev/min) corresponds to a period of (1.50s) so $$\mu_s=0.269$$

Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.

Cheenta. Passion for Mathematics

Advanced Mathematical Science. Taught by olympians, researchers and true masters of the subject.
JOIN TRIAL
support@cheenta.com