Question

A larger object is made of two balls separated by a massless rigid rod that is 1.5 m long. The mass of the red ball at one end is 1 kg and the mass of the orange ball at the other end is 5.7 kg. As in example 12.1, the balls are rotating about the center of mass. Calculate the speed of the 1 kg red ball if the angular velocity is 1 rev/s.

Answer 1

Answer:

The speed of the 1 kg red ball 8.04 m/s .

Explanation:

Given :

Separation between rods , d = 1.5 m .

Mass of the red ball is 1 kg .

Mass of the orange ball is 5.7 kg .

Angular velocity , $\omega=1\ rev/s = 2\pi\ rad/s$ .

Now , distance of center of mass  from red ball is :

$r =\dfrac{0\times 1+1.5\times 5.7}{1+5.7}\\\\r = 1.28\ m$

We know , speed is given by :

$v=\omega r\\\\v=2 \times \pi \times 1.28\\\\v=8.04\ m/s$

Hence , this is the required solution .