Confused: Net Torque vs Net Force

[aehardin]

I'm taking a mechanics course & I'm confused regarding the difference of Net Force & Net Torque. Net Force refers to linear motion & Net Torque refers to rotational motion, correct?

• So, is it possible to have a system where the net force is zero, but the net torque is not zero? For example, force being applied wrench trying to move a bolt.

• And vice versa, is it possible to have a system where the net torque is zero, but the net force is not zero? Like, if a square box was being pushed along the ground.

• And is it possible to have a system where both Net Force & Net Torque are not zero? For example, a car in a head on collision, where its tires are still rotating forward, but it's skidding backwards from the collision.

I'm not sure if I'm thinking of these concepts in the proper way. Any help, corrections to my thoughts, suggestions, or links to info would be greatly appreciated!

 

[Doc Al]

I'm taking a mechanics course & I'm confused regarding the difference of Net Force & Net Torque. Net Force refers to linear motion & Net Torque refers to rotational motion, correct?

Sounds good.

• So, is it possible to have a system where the net force is zero, but the net torque is not zero? For example, force being applied wrench trying to move a bolt.

Absolutely. One way is to apply two forces, equal and opposite but not acting on the same line. (These two forces form what is called a couple.) Imagine yourself pushing one side of an object while pulling the other (like turning a steering wheel with both hands); the net force is zero but it will rotate (assuming no other forces act to prevent it).

The problem with your example (force being applied to a wrench trying to move a bolt) is that if the bolt isn't turning, then the net torque (about its center) must be zero. Which just means that the wrench is not the only torque being exerted on the bolt.

• And vice versa, is it possible to have a system where the net torque is zero, but the net force is not zero? Like, if a square box was being pushed along the ground.

Since torque is always about some point, if there's a net force on an object you can always find some point about which there will be a torque. But you can certainly have a net force on an object that gives no torque about its center of mass. If you push that box with a force whose line of action goes through the center of mass, then you can exert a net force with no torque about the center of mass.

Another simple example is an object in free fall (ignoring air resistance): The net force (its weight) acts through its center of mass and thus exerts no torque about its center of mass.

• And is it possible to have a system where both Net Force & Net Torque are not zero? For example, a car in a head on collision, where its tires are still rotating forward, but it's skidding backwards from the collision.

Sure. But no need for such an involved example: Anytime you step on the gas and accelerate, there's a net force and a net torque on the tires. Or just roll a tire down a hill.

Going back to your sliding box: Imagine your box sliding on a frictionless floor. Exert any horizontal force you like on it, but just make sure it doesn't pass through the center of mass: you'll have a net force that will also exert a torque about the center of mass.

 

[arildno]

aehardin:
Doc Al has answered your main questions, but I'd like to say it's great you do your best in trying to understand the new concepts by looking at the various special cases. This is the way to go!

Keep up the good work, I'm sure you'll master these issues, and more, fairly quickly.