- #1
johne1618
- 371
- 0
Hi,
I was wondering if the formula for rotational energy:
E = 1/2 * L * w
where L is the angular momentum and w is the angular velocity,
is actually correct for relativistic velocities.
Using
L = p * r
and
w = v / r
where
p = the linear momentum = m * v
We get:
E = 1/2 * (m * v * r) * (v/r)
I would have thought that this expression is correct up to relativistic velocity as the expressions for linear momentum, p = m * v, and angular velocity, w = v / r, do not require relativistic modification provided that we acknowledge that m increases as v -> c.
As a corollary, as v -> c, it seems that the maximum rotational energy of a system is:
E = 1/2 * m c^2 (i.e. half the total mass/energy of the system)
John
I was wondering if the formula for rotational energy:
E = 1/2 * L * w
where L is the angular momentum and w is the angular velocity,
is actually correct for relativistic velocities.
Using
L = p * r
and
w = v / r
where
p = the linear momentum = m * v
We get:
E = 1/2 * (m * v * r) * (v/r)
I would have thought that this expression is correct up to relativistic velocity as the expressions for linear momentum, p = m * v, and angular velocity, w = v / r, do not require relativistic modification provided that we acknowledge that m increases as v -> c.
As a corollary, as v -> c, it seems that the maximum rotational energy of a system is:
E = 1/2 * m c^2 (i.e. half the total mass/energy of the system)
John
Last edited: