# Spinning rod dropping on a pivot

• mjolnir80
In summary, the problem involves a long, thin rod of mass M and length L standing vertically on a table with its lower end on a frictionless pivot. When given a slight push, the rod falls over and hits the table. The question asks for the angular velocity and speed of the tip of the rod. The suggested solution involves setting up a conservation of energy equation, considering only rotational kinetic energy and the potential energy of the center of mass.
mjolnir80

## Homework Statement

a long, thin rod of mass M and length L is standing stright up on a table. its lower end rotates on a frictionless pivot. a very slight push causes the rod to fall over. as it hits the table, what are (a) the angular velocity and (b) the speed of the tip of the rod?

## The Attempt at a Solution

could we set up a conservation of energy equation for this?
1/2I(for spinning of rod)$$\omega$$^2 + mgh = 1/2 I(for spinning of rod)$$\omega$$^2 + 1/2I(for dropping of rod)$$\omega$$^2

I'd suggest that there is only rotational kinetic energy to consider.

And it gets fed by the PE of the center of mass doesn't it?

Yes, we can use the conservation of energy equation to solve for the angular velocity and speed of the rod. We can also use the conservation of angular momentum equation, as the angular momentum of the rod will be conserved during the fall.

To solve for the angular velocity, we can use the conservation of energy equation you provided. We can set the initial energy (when the rod is standing straight up) equal to the final energy (when the rod is falling and rotating on the pivot). The initial energy will consist of the potential energy due to the height of the rod and the kinetic energy due to the spinning of the rod. The final energy will consist of the kinetic energy due to the rotation of the rod after it has fallen.

To solve for the speed of the tip of the rod, we can use the conservation of angular momentum equation. Since the angular momentum of the rod will be conserved during the fall, we can set the initial angular momentum (when the rod is standing straight up) equal to the final angular momentum (when the rod is falling and rotating on the pivot). The initial angular momentum will be zero, as the rod is not rotating initially. The final angular momentum will consist of the angular momentum due to the spinning of the rod and the angular momentum due to the rotation of the rod after it has fallen.

By setting up and solving these equations, we can determine the angular velocity and speed of the tip of the rod when it hits the table.

## 1. What is a spinning rod drop on a pivot?

A spinning rod drop on a pivot is a scientific phenomenon where a spinning rod, attached to a pivot point, is released from a horizontal position and allowed to rotate freely downward due to the force of gravity.

## 2. What causes a spinning rod to drop on a pivot?

The force of gravity is the main cause of a spinning rod dropping on a pivot. When the rod is released, the force of gravity pulls it downward and causes it to rotate around the pivot point.

## 3. What is the significance of studying spinning rod drops on a pivot?

Studying spinning rod drops on a pivot can help scientists better understand the principles of gravity, motion, and rotational dynamics. It can also have practical applications in engineering and design, such as in the development of pendulum clocks and other rotating devices.

## 4. How does the length of the spinning rod affect its drop on a pivot?

The length of the spinning rod can affect its drop on a pivot by changing its rotational speed and the distance it travels. A longer rod will have a longer drop and a slower rotational speed, while a shorter rod will have a shorter drop and a faster rotational speed.

## 5. Are there any real-world examples of spinning rod drops on a pivot?

Yes, there are many real-world examples of spinning rod drops on a pivot, such as pendulum clocks, playground swings, and amusement park rides. These all utilize the principles of gravity and rotational motion to create a repetitive and predictable motion.

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