Finding the Acceleration of a Rod in an X-Y Plane

[prat]

a rod is vertically placed in x-y plane
a slight disturbance is given to it so that it is inclined at an angle (90-a) with the horizontal.
find the acceleration of the centre of mass

i think that the path followed by the centre of mass would be elliptical so its acceleration can be gsina

 

[Mindscrape]

You need to find the inertia about the center of mass with respect to the axis that the rod is falling through.

 

[prat]

can you be more descripitive or suggest any way to solve the problem not understanding a bit

 

[Mindscrape]

Um, I personally feel like what I told you has been pretty descriptive. If you want more specifics then give more specifics to work with. I don't know what what's holding you up, I can't read minds. Say the rod rotates about x-axis, so find moment of inertia about the say x-axis (or the end of the rod), use conservation of energy for the center of mass, or torque, or lagrangian.

 

[paranormal]

in the direction of motion

I would like to clarify that the path followed by the centre of mass of the rod would not necessarily be elliptical. The acceleration of the centre of mass would depend on the specific properties of the rod and the nature of the disturbance applied to it.

To find the acceleration of the centre of mass, we can use the laws of motion and rotational dynamics. First, we need to determine the net force acting on the rod, which would include the force due to gravity, the normal force, and any other external forces. Then, using the equation F=ma, we can calculate the acceleration of the centre of mass in the x and y directions.

Additionally, since the rod is inclined at an angle with the horizontal, we would also need to consider the torque acting on the rod. This would involve calculating the moment of inertia of the rod and using the equation τ=Iα, where α is the angular acceleration. By finding the angular acceleration, we can then determine the acceleration of the centre of mass in the direction of the inclined angle.

In conclusion, the acceleration of the centre of mass of the rod in an x-y plane would depend on various factors and cannot be determined solely by the angle of inclination. Further analysis and calculations using the laws of motion and rotational dynamics would be necessary to accurately determine the acceleration.