What are the Rotational Dynamics of a Thin Rod Held by a Pivot Point and String?

In summary, the conversation discusses a problem involving a thin rod of length l and mass m that is fixed at one end by a free pivot and held from rotating with a string attached at 3/4l and fixed to a ceiling. The moment of inertia of the rod about the fixed end is ml2/3. The main question is solving for the angular acceleration of the rod after the rope is cut at t=0 seconds. The conversation also mentions finding the transverse acceleration of the rod's center of mass and point A (the far end of the rod), as well as the force exerted by the pivot point. The conversation includes a picture and some initial attempts at solving the problem.
  • #1
superaznnerd
59
0
rotational dynamics rod--please help!

Homework Statement


A thin rod of length l and mass m is fixed at a far ends by a free pivot and held from rotating with a string attached at 3/4l and fixed toa ceiling. The moment of inertia of a thin rod about a far end is ml2/3

a) what is the pivot point exerting on the rod

The rope is cut at t =0 seconds. at t =0 seconds find:
b) the angular acceleration of the rod.
c) the transverse acceleration of the rod's center of mass.
d) the transverse aceleration of point A (the far end of the rod)
e) the force exerted by the pivot point

picture is attached.
 

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  • #2


You have to at least try the problem and explain your thoughts before asking for help.
 
  • #3


First, total downward torque = upward torque.
.5mgl + Torque of pivot point = .75mgl
torque of pivot point = .25mgl.
This doesn't make sense because the pivot point can't exert a torque.
Thats all I got to...and I couldn't figure out anthing else lol
I have all the answers, I just need to understand hwo to do it.
 

Related to What are the Rotational Dynamics of a Thin Rod Held by a Pivot Point and String?

1. What is rotational dynamics and how does it apply to a rod?

Rotational dynamics is the study of the motion and behavior of objects that are rotating or spinning. It is a branch of classical mechanics that deals with the forces and torques acting on an object to produce rotational motion. In the case of a rod, rotational dynamics can be used to understand its movement and stability when rotated around a certain axis.

2. What factors affect the rotational dynamics of a rod?

The key factors that affect the rotational dynamics of a rod include its mass, length, shape, and the forces applied to it. The distribution of mass along the rod also plays a significant role in determining its rotational behavior.

3. How is torque related to rotational dynamics of a rod?

Torque is a crucial concept in rotational dynamics and is defined as the rotational equivalent of force. It is the measure of the twisting or turning force applied to an object. In the case of a rod, torque is responsible for producing rotational motion and can be calculated as the product of the applied force and the distance from the axis of rotation.

4. Can the rotational dynamics of a rod be affected by friction?

Yes, friction can play a significant role in the rotational dynamics of a rod. Frictional forces can oppose the motion of the rod and cause it to slow down or stop. Additionally, frictional forces can also affect the stability of the rod, especially if it is rotating at high speeds.

5. How can rotational dynamics of a rod be applied to real-world situations?

The principles of rotational dynamics can be applied to various real-world situations, such as the movement of a spinning top or the stability of a rotating helicopter blade. It is also essential in designing and understanding the behavior of objects such as wheels, gears, and turbines that rely on rotational motion for their function.

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