# Finding angular speed of a thin rod.

• Seraph404
In summary, the problem asks for the angular speed of a thin rod when it is vertical after falling from a horizontal position, assuming no friction and starting from rest. The solution involves using conservation of energy, considering the change in potential energy of the rod as its center of mass moves from a height of L to L/2. The correct answer is 5.4 rad/s.
Seraph404

## Homework Statement

A thin 1.0-meter-long rod pivoted at one end falls (rotates) from a horizantal position, starting from rest and with no friction. What is the angular speed of the rod when it is vertical?

## Homework Equations

I (of the thin rod) = (1/3)ML^2

## The Attempt at a Solution

I tried solving this problem using conservation of energy, but I'm not getting the right answer (5.4 rad/s).

For kinetic energy, I was using (1/2)I$$\omega$$^2; and for potential energy, I was using mgL. Then I solved for $$\omega$$. What's wrong with that?

In figuring out the change in PE of the rod, consider what happens to its center of mass.

It accelerates?

How does its position change? That determines the change in PE of the rod.

The CoM moves from a height of L to a height of L/2 ?

Good. So what's the change in PE of the rod?

MgL - Mg(L/2)

I got the answer now, thanks!

## 1. What is the formula for calculating the angular speed of a thin rod?

The formula for calculating the angular speed of a thin rod is ω = Δθ/Δt, where ω represents angular speed, Δθ represents the change in angle, and Δt represents the change in time.

## 2. How do you measure the angular speed of a thin rod?

The angular speed of a thin rod can be measured using a tachometer, which is a device that measures the number of rotations per unit of time. Another method is to use a stopwatch and measure the time it takes for the rod to complete one full rotation.

## 3. What factors affect the angular speed of a thin rod?

The angular speed of a thin rod can be affected by factors such as the length of the rod, the mass of the rod, the material of the rod, and the force applied to the rod.

## 4. Can the angular speed of a thin rod be negative?

Yes, the angular speed of a thin rod can be negative. This indicates that the rod is rotating in the opposite direction of the reference point or axis of rotation.

## 5. How is the angular speed of a thin rod related to its linear speed?

The angular speed of a thin rod is directly proportional to its linear speed. This means that the faster the rod rotates, the faster the linear speed of a point on the rod will be.

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