# Forces Producing Rotational & Translatory Motion: Exploring Mechanics

• NANDHU001
In summary, the conversation explores the mechanics behind why a force applied exactly perpendicular to one end of a rigid rod produces both translatory and rotational motion about the center of mass. This is due to the development of tension in the rod, which pulls both ends towards the center of mass. The thought experiment of two spherical bobs attached to an elastic string is used to illustrate this concept, as it also involves translation, rotation, and oscillation. The balance of centripetal forces at the center of mass is the key factor in understanding the mechanics behind this phenomenon.
NANDHU001
Why does a force applied exactly perpendicular to one end of a rigid rod produce translatory motion along with rotational motion about center of mass?
I know the mathematics F=m(center of mass)*a but I want a mechanical answer.
I think analyzing the following thought experiment will be of some help though i don't
know how to proceed with it.
Consider two spherical bobs attached to two ends of an elastic string.(rigid rod as a limiting case of elasticity)
When an exact perpendicular force is applied at one bob the bob will accelerate and move along a straight line while the other bob remains at rest. Now due to an increase in length
of the string a tension will be developed and will pull both the bobs toward its center of mass.
I don't know how to proceed with it and can't see why the rotation is about center of mass.

Why do you think it should not produce translatory motion? You push the rod in one direction. After your push, one end moves, the other does not, so the center of mass moves, too.

NANDHU001 said:
can't see why the rotation is about center of mass
Because you need a centripetal force for circular motion. At the center of mass the centripetal radial forces of both sides balance.

Thanks but please consider analyzing the thought experiment I have mentioned.

What is so special about that experiment? You will get translation, rotation and oscillation of the string length at the same time (assuming it has compression forces as well).

If the string does not give any force below a certain length, your objects will come closer, but miss each other until they extend the string again, and the whole thing repeats.

## 1. What is the difference between rotational and translational motion?

Rotational motion refers to the movement of an object around an axis, while translational motion refers to the movement of an object from one location to another in a straight line.

## 2. How are forces involved in producing rotational and translational motion?

Forces act on objects to produce motion. In rotational motion, a force must be applied at a distance from the axis of rotation, while in translational motion, a force must be applied in the direction of the motion.

## 3. What is the relationship between torque and rotational motion?

Torque is a measure of the force that causes an object to rotate around an axis. The greater the torque, the faster the object will rotate. Torque is calculated by multiplying the force applied by the distance from the axis of rotation.

## 4. How do you calculate the moment of inertia for an object?

The moment of inertia is a measure of an object's resistance to changes in rotational motion. It is calculated by multiplying the mass of the object by the square of its distance from the axis of rotation.

## 5. Can an object have both rotational and translational motion at the same time?

Yes, an object can have both rotational and translational motion at the same time. This is known as rolling motion, where an object rotates around an axis while also moving in a straight line.

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