Motion: Understanding Force Displacement

[IonAphis]

Arrrgh help!

There are 3 particles all with the same mass connected by rods to a central point all making 120 degrees with each other. All the rods are conected (kinda like making a triangle with little balls on the corners). So this thing is sitting in a plane, with no friction, just smooth surface. If I apply a force perpendicular to one of these little arms (rods) the body will start a free spin, and up to that point I understand. What I don't know is: after I apply the force, does the body displace (it's center of mass) on a straight line? or does applying force into one of the rods make it not only spin but also vector out? If so, how do I calculate this vector...
What you usually think it should do is displace, but wouldn't that be thanks to the friction? So really, if there is no friction, I should go on a straing line right?
Thanks for the advice in advanced
Ion Aphis

 

[Doc Al]

The applied force will cause the object to both translate and rotate:

(1) It will accelerate the center of mass of the object (balls + rods) per Newton's 2nd law: $\vec{F} = m \vec{a}$. Thus the center of mass will accelerate in the direction of the force. (If you maintain the force in a constant direction, it will move in a straight line.)

(2) It will exert a torque about the center of mass, imparting an angular acceleration per Newton's 2nd law for rotation: $\tau = I \alpha$​

 

[quicknote]

Hello Ion,

Thank you for your question. It seems like you have a system of particles connected by rods, forming a triangle shape. When a force is applied perpendicular to one of the rods, the system begins to spin freely. You are wondering if the center of mass of the system will also displace in a straight line or if there will be a vector component to its motion.

In this scenario, the force applied to the rod will cause the system to rotate around its center of mass. This means that the center of mass will not displace in a straight line, but rather it will follow a circular path. The direction of this circular path will depend on the direction of the force applied and the initial conditions of the system.

The concept of friction does not directly apply to this scenario since there is no surface for the system to slide or roll on. However, there may be some resistance due to air resistance or other factors, which could affect the motion of the system. In order to calculate the vector component of the motion, you would need to know the magnitude and direction of the applied force, as well as the initial conditions of the system such as its mass, moment of inertia, and initial angular velocity.

I hope this helps clarify the motion of the system in this scenario. Keep exploring and asking questions, that's how we scientists learn and make new discoveries! Best of luck with your studies.

Sincerely,