# Conservation of Energy for a rotating Rod

• AROD
In summary, the rotational kinetic energy of a uniform rod can be calculated using the equation 1/2*I*w^2, but the potential energy is MgL/2 due to the placement of the rod's center of mass at L/2 over the ground. The torque from gravity about the pivot point also depends on the angle of the rod. As the rod tips, the height can be calculated using the hypotenuse of L/2 and the cosine of theta.
AROD

## Homework Equations

Rotational Kinetic Energy = 1/2*I*w^2

## The Attempt at a Solution

I was just wondering if someone explain to me why the potential energy is MgL/2 ?

Is this not the same for the torque from gravity?

As the hint in a) states, you can neglect the mass m. And since the mass M is uniform, you can presume all its weight is in the center, hence MgL/2

Because the rod's center of mass is placed at L/2 over the ground.

AROD said:
I was just wondering if someone explain to me why the potential energy is MgL/2 ?
The rod is uniform. Where is its center of mass?
Is this not the same for the torque from gravity?
The torque from gravity about the pivot point depends upon the angle of the rod.

ok so then its just mgh with h = L/2 . that makes sense

then as it tips the hypotoneuse would be L/2, and the height would be this times the cos of theta.

thanks

## 1. What is the conservation of energy for a rotating rod?

The conservation of energy for a rotating rod is a principle in physics that states that the total energy of a rotating rod remains constant as long as there are no external forces acting on it. This means that the kinetic energy and potential energy of the rod will remain constant, even as the rod rotates.

## 2. How does the conservation of energy apply to a rotating rod?

The conservation of energy applies to a rotating rod because the energy of the rod is conserved as it rotates, meaning that no energy is lost or gained. This is due to the fact that the rod's potential energy is converted into kinetic energy as it rotates, and vice versa.

## 3. What is the equation for calculating the conservation of energy for a rotating rod?

The equation for calculating the conservation of energy for a rotating rod is E = 1/2Iω^2 + mgh, where E is the total energy, I is the moment of inertia of the rod, ω is the angular velocity, m is the mass of the rod, g is the gravitational acceleration, and h is the height of the rod.

## 4. How does the conservation of energy affect the motion of a rotating rod?

The conservation of energy affects the motion of a rotating rod by keeping the total energy of the rod constant, which in turn affects the speed and direction of its rotation. As the rod rotates, the conversion between potential and kinetic energy ensures that the total energy remains constant.

## 5. What are some real-world examples of the conservation of energy for a rotating rod?

Some real-world examples of the conservation of energy for a rotating rod include a spinning top, a Ferris wheel, and a planet orbiting around a star. In each of these examples, the energy of the rotating object is conserved, and the speed and direction of rotation remain constant as long as there are no external forces acting on the object.

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