Question about rotational and translational equilibrium

[sillyjoe]

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If the net force on an object is zero, what can you conclude?


A. The object is in translational equilibrium only
B. The object is in rotational equilibrium only.
C. The object is in both translational and rotational equilibrium.
D. The object is stationary.

Choice A is the best answer. The only thing we are able to conclude is that the object is in translational equilibrium. Choice B is incorrect: A net torque of zero is required for the system to be in rotational equilibrium. Choice C is incorrect: A net force of zero does not imply a net torque of zero, because the component forces may be acting in an asymmetric fashion about the system's center of mass, resulting in a net torque on the system. Choice D is incorrect: Translational equilibrium means no linear acceleration, but the object could still be moving with a constant linear velocity (keeping in mind Newton's first law that an object at rest will remain at rest and an object in motion will remain in motion unless there is a net force acting on it). The best answer is choice A.

If the object has a torque but no net force isn't the object going to be going in a circular motion and therefore have a force acting on it? Why is this system considered to be in translational equilibrium?

 

[BerkReviewTeach]

Circular motion is caused by a torque, not by a force. Linear acceleration results from a net force. That force can result in a torque if applied perpendicular to a moment arm (distance from point of applied force to the fulcrum), but that does not result in a net force on the object. Think of a tire on an upside-down bicycle. You can brush your hand against the tire to get it to spin, but the entire bike (tire included) stays in the same place (its center of mass does not move). This is because the pushing on the tire was done at a point where you are pushing on a moment arm connected to a fulcrum and not moving the system.

 

[sillyjoe]

Circular motion is caused by a torque, not by a force. Linear acceleration results from a net force. That force can result in a torque if applied perpendicular to a moment arm (distance from point of applied force to the fulcrum), but that does not result in a net force on the object. Think of a tire on an upside-down bicycle. You can brush your hand against the tire to get it to spin, but the entire bike (tire included) stays in the same place (its center of mass does not move). This is because the pushing on the tire was done at a point where you are pushing on a moment arm connected to a fulcrum and not moving the system.

Just for clarification then, why is the centripetal acceleration of rotational motion that is occurring in your bicycle not a result of a net force?

 

[BerkReviewTeach]

Ask yourself, "Is the center of mass for your bicycle changing?" In order to have an acceleration of an object that is initially at rest, the center of mass must move (that is to say, there must be some displacement). Even though the tire spinning, the bike is not moving, so there has been no displacement, so the velocity has remained at zero. If the velocity remains at zero, then there is no acceleration. If there is no acceleration, then there is no net force acting on the object.