Angular and linear momentum?

Question

Hey, can someone explain the relationship between linear and angular momentum. I know the equations p=mv (for linear momentum) and L=rp (for angular momentum). So how do i find out the linear speed of an object that's being spun around a center point. Say a disk of 500 kg of radius 1 meter being spun around once every second. So how do i find out the v in p=mv to find out the angular momentum ?
The simpler the help the more the thanks.

Answer 1

the linear momentum for a single particle is p=mv, it is also valid for an object as long as all particles in the object have same velocity v.
the angular momentum for a particle is L=rp, no matter this particle is moving or spinning.
For a disk that is composed of many particles, its angular momentum is the sum of angular momentum of all particles. We can derive an another formula L=Iw where I is moment of inertia and w is the angular velocity.
Now for the disk in the question I=mr^2/2=500*1^2/2, w=2*pi*(frequency)=2*pi*1
so the angular momentum of the disk is 500*2*pi/2=1.57 x 10^3 kgm^2/s

Answer 2

When you look at it real close, there is no difference. Both are momentum. As you put it p = mv, the linear momentum of a mass m going at a linear velocity v. We call this "linear" because there is no twisting of the body m.

And, interestingly, angular momentum is also P = mV, but, and this is a big BUT, the V is not a linear velocity it is a tangential velocity. That is, V is now going perpendicular to the radius of rotation...and rotation is what gives us the angles for "angular." As V is tangential, P is also tangential; it, too, has a vector perpendicular to the radius r of the spin.

And because of that radius, there is a rotation or turning, and the momentum turns around the rotational axis r distance away. Thus we add that moment arm r to mV and get L = rmV = rP, with the understanding that P, and V, are acting perpendicular to r.

So, for a given m, which is spinning around on a fixed radius r, we have L = rP = rmV = rmwr = mwr^2; where V = wr and w is the angular velocity in radians per unit time. L is the angular momentum of that same mass m that had the linear momentum. But this time it's rotating around an axis some r distance away.

If we think of the m as being some small element of mass and mentally construct your disk of a lot of elements of that mass, we will have each element contributing an element of angular momentum. Through a calculus technique called integration, we can mathematically add up all those elements of angular momentum to find the angular momentum of a solid disk.

That turns out to be L = 1/2 MwR^2 [See source]; where M is the mass of the disk, w is the angular velocity, and R is its radius. Looks a lot like the equation for the elemental m doesn't it? The factors 1/2 MR^2 = I have a special name...the moment of inertia. So, we can write L = wI; where we can see that the w and I take the places of v and m in p = mv.

Now, had you asked to find V, the tangential velocity in L = rmV that would be V = wr; where w = 2pi per sec and r = 1 meter; so that V = 2pi*1 = 2pi meters per sec. But that's not the v in p = mv.

Now to your problem. You cannot find v in p = mv, the linear momentum, because v is not tangential v, it is the linear v. For example, presume the disk mass is M. If its center of mass (at the axis of rotation) were moving at linear velocity v while the disk was spinning at angular velocity w = V/R, the disk would have both linear and angular momentum. But as you can reason yourself, there is no linkage between v and V = wR.

Answer 3

Velocity or momentum of a solid object or a point particle can be thought of relative to the observer. When you talk of angular momentum you have to give one more information and that is about which point. Take the case of the spinning disc about its centre point. If you ask me what is the velocity of the disc. If by disc you mean its centre point obviously it is zero. But is the velocity of every point of the disc zero? Obviously not. Every point of the disc other than centre point is having some velocity which is different in direction at least. But for all points the angular velocity, w about the centre point is same.; So angular momentum of every point is (mr^2)x(w), where m is the mass of the point on disc and r its distance from centre point. If you add all these you would get {(MR^2)/2]xw. This is called the angular momentum of the disc about the centre point. Obviously the angular momentum depends upon the point of reference.

Answer 4

Angular momentum is likewise a scalar. however: angles themselves are actually not vectors. you are able to prepare that angles a, b and c, in the event that they are orthogonal to a minimum of one yet another, provide diverse reulting angles for a+b+c vs. a+c+b, as an occasion.