Question

Imagine you have a spinning mass (holded by a massless string say). And you increase the radius of the string with a constant rate, at the same time than exerting a perpendicular force on the mass so as to keep the angular velocity constant. Then tangential acceleration of the mass should be w*r' where w is angular velocity and r' is the time derivative of the radius. Also the change in angular momentum is 2*m*r*r'*w, and that is equal to the torque, which is F*r. So te force exerted is 2*m*r'*w, and the acceleration, 2*r'*w. How come this is double?

Answer 1

You say "Then tangential acceleration of the mass should be w*r' ".
This is the |v|' - but explain why this is necessarily tangential ?

Answer 2

@guillefix ?

Answer 3

Hm I thought that w*r is the tangential velocity, and its derivative should be the tangential acceleration, shouldn't it?

Answer 4

No it is all vector expressions and their differentials are generall y bot tangential and radial

Answer 5

See here
http://www.real-world-physics-problems.com/curvilinear-motion.html

Answer 6

Here I think you were right - this one is clear for this

Answer 7

So you agree?. My line of thought was: acceleration of tangential velocity=(w*r)'=r'*w+w'*r, but as I defined w' to be 0 i was only left with the first term

Answer 8

¿? My question hasn't been answered

Answer 9

Yes, well you are right.

Answer 10

But my question was that using change in angular momentum it didn't give the same result.

Answer 11

i.e., the force applied to keep the angular velocity the same while having a radial velocity is: 2*m*r'*w, which differs from what you'd expect due to the factor of two

Answer 12

Angular momentum (L) only applies to objects that are spinning, but just like linear momentum, it is always conserved, that is, unless some external torque is applied to the object. Also like linear momentum, there are two main ways to define angular momentum: the cross product between the vector distance from some origin (r) and the linear momentum [L = r x p], or the product of the moment of inertia (I) and the angular velocity (w) [L = I*w]. The first definition is a more broad definition because the second only applies to a rotation around a fixed symmetry axis. The second definition uses moment of inertia, which is a complicated number found as the sum of every particle in the object's mass times the particle's distance from the rotation axis squared. To simplify this, equations for moment of inertia for typical objects are normally just memorized. Angular velocity (which is written with a lower-case omega and not really a 'w') is the change in angle per time. It is most typically found by dividing tangential velocity by the radius. Angular momentum has units of mass-distance-squared per time or force-distance-time which is kilogram-meters-squared per second (kg*m^2/s) or Newton-meter-seconds (N*m*s) in SI. As notable from the cross product involved in finding angular momentum, is an axial vector, or pseudovector, which means it would have direction perpendicular to the plain of rotation, most simply found by the "right hand rule."