Question

A thin rod can rotate freely through an off-center axis. The rod has a length of l = 4ℓ = 1.0 meter and has a mass of m = 0.5 kg. The rod is allowed to freely rotate vertically through a point located at length ℓ = 0.25 meters measured from its "left" side. Two masses are then attached by massless/unbreakable cords.

Answer 1

To solve this problem, we use the principle of conservation of angular momentum. By calculating the angular momentum of each weight separately and setting their sum equal to zero, we can solve for the unknown distance d.

Step-by-step explanation:

To solve this problem, we need to use the principle of conservation of angular momentum. When the rod is released, it will start rotating due to the weights attached to it. The total angular momentum before releasing the rod is zero since it is at rest. After releasing, the angular momentum will be conserved.

We can calculate the angular momentum of each weight separately by using the formula L = Iω, where L is the angular momentum, I is the moment of inertia, and ω is the angular velocity.

Finally, we can set the sum of the angular momenta of the two weights equal to zero and solve for the unknown distance d:

d = (m2l2 - m1l1) / (m1 + m2)