# Analyzing Rotational Motion of Massless Rod and Object

• beardedone85
In summary, the problem involves a mass-less rod of length Ls rotating clockwise about a point P1 in the horizontal plane. Attached to the end of the rod, at an angle θ, is an object of mass M. The object starts at rest and then experiences an angular acceleration α. The conservation of angular momentum and the relationship between linear and rotational kinetic energy are relevant in solving this problem. The tension in the sling is a key factor, but relating the translation of the rod tip to the translation of the object proves to be a challenge. Suggestions for solving this problem include using similar triangles and considering the direction of the acceleration.
beardedone85

## Homework Statement

A mass-less rod of length, Ls, is rotating clockwise about a point, P1 in the horizontal plane. Attached by a cable of length, Ls, to the end of the rod and at angle θ is an object of mass, M. Starting at rest and then with the rod having and angular acceleration α, describe the motion of the object.

I am attempting to make a trebuchet simulator and I am stuck of this part. If I could figure out the motion in this simplified example I feel I can add gravity and all of the variables that will effect α.

A picture can be seen here:
http://www.flickr.com/photos/34636154@N08/6798503780/

## Homework Equations

It seems to me that the conservation of angular momentum, r*MV, and relating Linear Kinetic energy KE = 1/2MV^2 with rotational Kinetic energy KEr = 1/2Iω^2 would be the way to go. The problem for me appears to be in figuring out what the tension in the sling will be. F=ma=T(tension) but how do I relate the translation of the rod tip to the translation of the object?

## The Attempt at a Solution

I had attempted to take the acceleration tangential of the rod tip and set it equal to the acceleration of the object in the same direction, similar to how if this was a static problem and we knew the force perpendicular to the arm we could then find the tension in the sling by using similar triangles, but that seemed to give me some pretty strange numbers, plus it would mean that if the arm was experiencing a negative α, the projectile would also decelerate, which is not correct.

I am sure that this is a fairly simple problem, but I am stuck. Any help would be greatly appreciated.

## What is rotational motion?

Rotational motion is the movement of an object around an axis or center point. It is different from linear motion, where an object moves in a straight line.

## What is a massless rod?

A massless rod is a hypothetical object that has no mass but is rigid enough to maintain its shape and transfer forces. It is often used in physics problems to simplify calculations.

## How is rotational motion analyzed?

Rotational motion is analyzed using various equations and principles from rotational dynamics, such as torque, angular velocity, and angular acceleration. These equations can be used to calculate the motion of objects in rotational motion.

## What is the moment of inertia?

The moment of inertia is a measure of an object's resistance to rotational motion. It depends on the mass and distribution of mass around the axis of rotation. The greater the moment of inertia, the harder it is to rotate an object.

## What factors affect the rotational motion of a massless rod and object?

The rotational motion of a massless rod and object can be affected by several factors, including the mass and distribution of mass of the object, the distance from the axis of rotation, and the torque applied to the object. Friction and air resistance can also affect rotational motion.

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