Tangent force on a rotating rod

In summary, the conversation discusses a problem involving a falling rod and finding the tangential component of the force exerted on the upper part of the rod. The solution involves determining the angular acceleration and the moment of inertia, and eventually focusing on the center of mass to find the net force.
  • #1
abomination5
5
0

Homework Statement


I've been working on this problem for several hours with no luck. Any help would be appreciated. (It's not homework)

A thin rod of mass M and length L is hinged at the bottom, and almost balanced vertically. It starts to fall. Find the tangential component of the force that the part of the rod below r exerts on the part of the rod above r.

(Theta is the angle between the rod and the vertical, r is the distance on the rod from the hinge)


Homework Equations



SOLN: F = Mg(L-r)(3r-L)/(4 L^2) * Sin(theta)

d x F = I *(angular acceleration)


The Attempt at a Solution



I've already determined the angular acceleration to be

3/2 g/L Sin(theta)

using the Lagrangian.

I've calculated the moment of inertia to be:

1/3 M (L-r)/L [(L-r)^2 + 3*r^2]

using the parallel axis theorem.

I've tried for several hours to get the final equation for the force but I haven't been able to do so yet... maybe there is a mistake in the moment of interia?
 
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  • #2
abomination5 said:

The Attempt at a Solution



I've already determined the angular acceleration to be

3/2 g/L Sin(theta)
Good.

using the Lagrangian.

I've calculated the moment of inertia to be:

1/3 M (L-r)/L [(L-r)^2 + 3*r^2]
Rather than go this route, focus on the center of mass of the piece in question. What is its acceleration? What must be the net force on it?
 
  • #3
Doc Al,

Thanks for your help. I was able to get the solution this morning. I won't spoil the rest of the details for anyone who wants to try it.
 

1. What is tangent force on a rotating rod?

Tangent force on a rotating rod is the force acting on an object that is perpendicular to the object's motion. In other words, it is the force that is tangent, or at a right angle, to the direction of motion.

2. How is tangent force related to centripetal force?

Tangent force is directly related to centripetal force, as it is the component of centripetal force that acts perpendicular to the object's motion. Without a tangent force, an object would not be able to maintain its circular motion.

3. What factors affect the magnitude of the tangent force on a rotating rod?

The magnitude of the tangent force on a rotating rod depends on the mass, speed, and radius of the rotating object. The greater the mass, speed, or radius, the larger the tangent force will be.

4. How is tangent force calculated?

Tangent force can be calculated using the formula F = mv²/r, where F is the tangent force, m is the mass of the object, v is the speed, and r is the radius of the rotating object.

5. Can tangent force cause an object to leave its circular path?

Yes, if the magnitude of the tangent force is greater than the centripetal force, an object can leave its circular path and move in a straight line. This is known as the "tangent force problem" and can be solved by adjusting the speed or radius of the rotating object.

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