Question

A) Juan is sitting on the edge of a platform that rotates at a rate of 20 revolutions per minute. The platform has a 4.5m radius. What is the linear speed in which Juan moves? What is the moon's period?

Answer 1

Respuesta:

First of all, Juan's angular velocity must be expressed in SI units:

20\frac{\cancel{rev}}{\cancel{min}}\cdot \frac{2\pi\ rad}{1\ \cancel{rev}}\cdot \frac{1\ \cancel{min}} {60\ s} = \frac{2\pi}{3}\frac{rad}{s} = 2.1\ s^{-1}

a) Juan's speed can be expressed as the product of the angular speed by the radius:

v = \omega\cdot R = 2.1\ s^{-1}\cdot 4.5\ m = \fbox{\color{red}{\bm{9.45\ \frac{m}{s}}}}b) The period of its motion is:

\omega = \frac{2\pi}{T}\ \to\ T = \frac{\cancel{2\pi}\ \cancel{rad}}{\frac{\cancel{2\pi}}{3 }\frac{\cancel{rad}}{s}} = \fbox{\color{red}{\bm{3\ s}}}

Explicación: