Question

A 100g ball and a 200 g ball are connected by a , 30- cm long massless, rigid rod. The balls rotate about their center of mass at 120 rpm. What is the speed of the 100 g ball?

Short answer

The speed of the 100 g ball is $v_1=2.5\text{m}/\text{s}$

Step-by-step solution

Step 1. Given information

A distance between balls, $30\text{cm}$, an angular velocity $120\text{rpm}$, and the mass for each ball.

Step 2. Explanation

The center of mass of the two balls measured from the left hand ball is

$x_{\text{cm}}=\frac{(100\text{g})(0\text{cm})+(200\text{g})(30\text{cm})}{100\text{g}+200\text{g}}=20\text{cm}$

The linear speed of the ball is

$\begin{array}{l}{v}_1=r\omega =x_{\text{cm}}\omega \\ v_1=(0.20\text{m})(120\text{rev}/\text{min})\left(\frac{2\pi \text{rad}}{\text{rev}}\right)\left(\frac{\text{min}}{60\text{s}}\right)\\ v_1=2.5\text{m}/\text{s}\end{array}$

Therefore, the speed of the 100g ball is$v_1=2.5\text{m}/\text{s}$