- #1
CollinsArg
- 51
- 2
Why the tangential velocity of a particle increase if there are no external torque acting on it and its angular momentum is conserved?
I know that L = I.ω (angular momentum equals moment of inertia times angular velocity)
and v = ω.r (tangential velocity equals angular velocity times the position of the particle), then ω = v/r
doing substitution ⇒ L = I.v/r
Also I know I = m.r2 (supposing for one particle, the mass of the particle times its position)
Then L = m.r2.v/r ⇒ L = m.r.v
Because the angular momentum is conserved v = L/m.r
Hence, as I change the position of the particle (the same as the radius of the circumference) its velocity changes without any torque being applied, why is it so? Shouldn't velocity be always constant? What does make its velocity change if I can see only a centripetal force (and I learned that centripetal forces can only change the direction of the vector velocity)? Thanks.
I know that L = I.ω (angular momentum equals moment of inertia times angular velocity)
and v = ω.r (tangential velocity equals angular velocity times the position of the particle), then ω = v/r
doing substitution ⇒ L = I.v/r
Also I know I = m.r2 (supposing for one particle, the mass of the particle times its position)
Then L = m.r2.v/r ⇒ L = m.r.v
Because the angular momentum is conserved v = L/m.r
Hence, as I change the position of the particle (the same as the radius of the circumference) its velocity changes without any torque being applied, why is it so? Shouldn't velocity be always constant? What does make its velocity change if I can see only a centripetal force (and I learned that centripetal forces can only change the direction of the vector velocity)? Thanks.