# Forces Acting on a Rod in Empty Space: Motion & Kinetic Energy

• HelloWorld2
In summary: In short, a rod will rotate about its centre of mass due to the applied force. The rotational kinetic energy of the system is the sum of the rotational kinetic energy of the rod and the rotational energy of the particles it is rotating around. α is the rotational acceleration of the rod.
HelloWorld2
Suppose I have a metal rod in empty space with a uniform mass distribution. Suppose a force acts perpendicular to the rod at some distance R from the rod's centre of mass over some time Δt. There are no other forces acting on the rod.

(1) What type of motion will the rod have over Δt? Will the rod rotate about the point where the force acts, or will it have some other type of motion?

(2) How much of the work done on the rod will be converted to translational kinetic energy and how much will be converted to rotational kinetic energy?

Note that the force does not change direction even as the rod rotates - ie it only acts perpendicular to the rod at the start of its motion.

Thank You.

BTW - This question is theoretical in nature - ie it doesn't require a calculation so I don't think it counts as a "homework" type question. I've been thinking about this for some time now. Nevertheless, I apologise if I've placed it in the wrong section.

HelloWorld2 said:
Suppose I have a metal rod in empty space with a uniform mass distribution. Suppose a force acts perpendicular to the rod at some distance R from the rod's centre of mass over some time Δt. There are no other forces acting on the rod.

(1) What type of motion will the rod have over Δt? Will the rod rotate about the point where the force acts, or will it have some other type of motion?

(2) How much of the work done on the rod will be converted to translational kinetic energy and how much will be converted to rotational kinetic energy?

Note that the force does not change direction even as the rod rotates - ie it only acts perpendicular to the rod at the start of its motion.

Thank You.

BTW - This question is theoretical in nature - ie it doesn't require a calculation so I don't think it counts as a "homework" type question. I've been thinking about this for some time now. Nevertheless, I apologise if I've placed it in the wrong section.

Welcome to the PF.

Are you familiar with Free Body Diagrams (FBDs)? Are you familiar with moments and the Moment of Inertia (MOI) of a rod?

We've just covered basic mechanics at uni (I'm doing first year physics). We've finished all topics in both the translational and rotational aspects of mechanics, including force diagrams and rotational inertia.

I know that the angular acceleration of the rod will be the quotient of the acceleration and the distance the force was exerted from the centre of mass. From here we can find the angular velocity after Δt, hence the rod's rotational kinetic energy. We can then subtract the rotational kinetic energy from the total work done to the system to find the translational kinetic energy.

After I've removed the force the rod will move in a straight line and rotate about its centre of mass, but what will be its motion over Δt? And why does the rod gain rotational acceleration equal to α / R? I can calculate how much rotational energy the system gains only once I know that this statement is true (I want to know why its true).

Thank you

## 1. What is a force?

A force is a push or pull that can cause an object to accelerate or change its motion. It is a vector quantity, meaning it has both magnitude (strength) and direction.

## 2. How many forces can act on a rod in empty space?

In empty space, a rod can experience up to three different forces: gravity, electromagnetic force, and contact force. However, if the rod is stationary, it will only experience the force of gravity.

## 3. How does the motion of a rod in empty space change when different forces act on it?

The motion of a rod in empty space is determined by the net force acting on it. If there is no net force, the rod will remain in a state of constant motion (either at rest or moving with constant velocity). If there is a net force, the rod will accelerate in the direction of the force.

## 4. How is kinetic energy related to the forces acting on a rod in empty space?

Kinetic energy is the energy an object possesses due to its motion. The amount of kinetic energy an object has is directly proportional to its mass and the square of its velocity. Thus, the forces acting on a rod in empty space can change its kinetic energy by altering its velocity.

## 5. Can a rod in empty space have kinetic energy if there are no forces acting on it?

No, a rod in empty space cannot have kinetic energy if there are no forces acting on it. Kinetic energy is a result of motion, and without any forces causing the rod to move, it will have no kinetic energy.

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