Understanding Torque, Circular Motion, and Momentum: Physics Help for Beginners

[Riya]

this is my first time taking physics and I'm regretting as to why i took it...My teacher is not at all helpful... he never quizzes us...to help us he think itz a waste of time...

so please help me understand these:
-torque
-circular motion
-momentum

thankyou

 

[Diane_]

The question is a little general for a medium like this. Let's see if this helps:

Torque - well, do you understand force? Forces cause things to accelerate linearly, i.e. in a straight line. Torques are the rotational analogues of forces. Torques are "twisting forces" - they cause things to accelerate in a rotational way. Either of them can be used to provide the other. For instance, on a merry-go-round (which I think is called a "roundabout" outside the US), you start the thing going by pushing on the outside. The push you apply is a force - it tends to make the outside of the merry-go-round accelerate. Since the outside is attached by the structure of the merry-go-round to the center, there is a moment arm between where you apply the force and the center. Consequently, your force provides a torque to start the merry-go-round rotating.

Similarly, the transmission in your car provides a torque to the driving wheels. That torque, through friction between the tires and the road, ends up providing a force that accelerates your car down the road.

General rule: Forces provide accelerations, accelerations are provided by forces. Any time something is accelerating, there's a force involved. Any time there's an unbalanced force involved, there will be an acceleration.

Torques provide "angular accelerations" - accelerations that cause rotations - and angular accelerations are provided by torques. Any time something experiences an angular acceleration, there is a torque involved. Any time there is an unbalanced torque involved, there will be an angular acceleration.

Circular motion: I'm afraid that's just too vague, luv. I have about three weeks worth of lectures on the topic. Can you be a little more precise?

Momentum: The product of mass and velocity. Momentum is a vector quantity, which means that direction matters. It's primary importance comes from the fact that it's one of the few quantities which is absolutely conserved, meaning that you never create or destroy any of it. If some part of a system acquires a certain amount of momentum in one direction, some other part of the system must acquire the same amount in the exactly opposite direction to cancel it out.

So much for that. It's a little off, but you might think of momentum as how hard it will be to stop something or change its course. A styrofoam pellet moving at very low speeds would be very easy to stop or deflect - it has very little momentum. A fully-loaded eighteen-wheel truck traveling at 100 km/hr would be very hard to stop or deflect - it has a lot of momentum. If you did manage to stop the truck, you would have to transfer its momentum to something (or some things) else. The momentum won't go away - you have to do something with it. That's more or less what "absolutely conserved" means.

Note that this makes momentum very useful for predicting the outcome of collisions and things. If you know the mass and velocity of everything coming into the problem, then you know the total momentum at the start. This means you also know the total momentum afterwards, because they must be the same.

A case in point: in the early days of particle physics, certain particles were observed to decay, or (in this case) break up into other, smaller particles. In every case, these smaller particles were observed to move off to one side of the original particle. It would be as though a firecracker were to explode, and every piece of it suddenly headed north. Common sense says this won't happen with the firecracker - conservation of momentum says this couldn't be happening with the particle. The conclusion was that there was an unseen component to the particle decay which was moving off in the opposite direction. Careful measurement of the momenta of the observed fragments gave a good figure for the momentum of the unobserved fragment(s). This data was among the first proof of the existence of something called a 'neutrino'.

Does any of this help? At all?

 

[cepheid]

I take it you have the definitions of these quantities your book, and are just trying to get a sense of what they represent? I will try my best:

Circular motion is the easiest, for it is exactly what its name suggests. A particle in circular motion about some point at a constant speed is being subjected to an force pointing inward, towards the centre (a centripetal force), and therefore has a centripetal acceleration. The acceleration does not affect the particle's speed, only its direction. It "wants" to move off in a straight line (Newton's first law), but the force keeps it moving in a circle about that centre point.

An example is a ball on a string being swung. The string tension is a centripetal force that keeps the ball moving in a circle about the point at which you're holding the string. Let go of the string, and this tension force vanishes, so the ball moves off in a straight line. Another similar example is an object in orbit...the gravitational force acts toward the centre of the circular orbit...keeping the object in that orbit.

If you're wondering why the force, and therefore the accelaration, is radial (ie centripetal), draw a circle. Notice that for an object to move on that circular path, its velocity has to be tangent to the circle at every point you consider. Therefore, the velocity vector is changing direction constantly. It always seems to rotate in a direction "towards the centre" of the circle. Therefore, the object's acceleration (which causes the change in the velocity vector) points toward the centre.

Finally, note that an object in circular motion with a changing speed has both a tangential component of acceleration (which speeds or slows the object) and a radial component. Combine the two, and you'll see that the total acceleration is still pointing inside the circle, just not directly toward the centre anymore, part of it is in the direction of motion.

Edit: Nice! That worked out well. I ended up discussing what Diane did not. It was pure chance. I agree with her that this is a big topic though.

 

[Riya]

thanx a ton guyz that really really helps :)