Rotation induced by moving center of mass

In summary, adding mass to one of the beams in a system connected by servo motors will cause the system to rotate as the center of mass is no longer centered. The equation of angular acceleration can be used to model this rotation, taking into account the mass and distance from the axis of rotation.
  • #1
erabenda
1
0
Two identical uniform beams are connected together by a set of servo motors. When the motors activate the two beams will come together uniformly and the center of mass of the system will move outward along the arrow shown. I would expect that the torque exerted by the motors would only cause the beams to rotate around each other through the axis that runs through the servo.

Now, if mass is added to the end of one of the beams so that the center of mass is no longer centered in the system. When the motors are now activated the beams will move together, but the motion will not be uniform. The lighter beam will move through a greater angle. In addition I would expect for the entire system to rotate as shown by the blue arrow. What equation describes this rotation or how could this rotation be modeled?

I am ignoring any external forces such as gravity

Thank you
 

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  • #2
for your question. The equation you are looking for is the equation of angular acceleration. This equation is given by the following: α = τ/I , where τ is the net torque applied to the system and I is the moment of inertia of the system. The moment of inertia is a measure of an object's resistance to angular acceleration and is given by the following equation: I = mr2 , where m is the mass of the system and r is the distance from the axis of rotation. Therefore, the angular acceleration of the system when the motors are activated will be proportional to the torque applied by the motors and inversely proportional to the mass and distance from the axis of rotation.
 

1. What is rotation induced by moving center of mass?

Rotation induced by moving center of mass is a phenomenon that occurs when an object or system experiences a change in its rotational motion due to a shift in its center of mass. This can happen when an external force is applied to the object, causing it to move in a linear direction and consequently changing its center of mass.

2. How does rotation induced by moving center of mass affect an object's stability?

This phenomenon can affect an object's stability in two ways. First, if the change in center of mass causes the object to rotate in a different direction, it may become unbalanced and lose stability. Second, the rotational inertia of the object may also change, affecting its ability to resist external forces and maintain stability.

3. Can rotation induced by moving center of mass be controlled?

Yes, rotation induced by moving center of mass can be controlled by adjusting the external forces acting on the object. For example, a gymnast can control their rotation in the air by changing the position of their limbs to shift their center of mass.

4. What are some real-world examples of rotation induced by moving center of mass?

This phenomenon can be observed in many sports and activities, such as gymnastics, figure skating, and diving. It is also important in engineering and design, as it can affect the stability and performance of vehicles and structures.

5. How is rotation induced by moving center of mass related to angular momentum?

Rotation induced by moving center of mass is related to angular momentum through the conservation of angular momentum principle. When an external force shifts the center of mass of an object, the object's angular momentum will also change to maintain the total angular momentum of the system. This can result in a change in the object's rotational motion.

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