Answer:
5.160384 kg*m²/s
Explanation:
The vector angular momentum P can be found using the following expression:
P = I * w
I refers to the inertia, that for a sphere is found using the expression:
I = * m * r² =
* 15.5kg * (0.510m)² = 1.61262 kg*m².
The angular velocity w is given by the problem, and has a value of 3.2 rad/s.
Replacing the data we get:
P = 1.61262 kg*m² * 3.2 rad/s = 5.160384 kg*m²/s
(a) The angular speed of the system at the instant the beads reach the end of the rod is 9.26 rad/s.
(b) The angular speed of the rod after the after the beads fly off the rod's ends is 25.71 rad/s.
<h3>Moment of inertia through the center of the rod</h3>I = ¹/₁₂ML²
I = ¹/₁₂ (0.1)(0.5)²
I = 0.0021 kgm²
For the beads, I = 2Mr² = 2(0.03 x 0.1²) = 0.0006 kgm²
Total initial moment of inertia, Ii = 0.0021 kgm² + 0.0006 kgm²
I(i)= 0.0027 kgm²
When the beads reach the end, I = 2Mr² = 2(0.03)(0.25)² = 0.00373 kgm²
Total final moment of inertia, I(f) = 0.0021 kgm² + 0.00373 kgm²
I(f) = 0.00583 kgm²
<h3>Speed of the system</h3>The speed of the system at the moment the beads reach the end of the rod is calculated as follows;
Learn more about moment of inertia of rods here: brainly.com/question/3406242