1
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3answers
99 views

Integral ambiguity

I'm a bit confused with some notation I encounter in physics calculus. Consider this: Taken from here. Integration operates on functions, correct? What does it mean to integrate $\frac{d{\bf ...
1
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1answer
44 views

calculating electrodynamic momentum of a dumbbell (consisting of two point charges) in longitudinal motion

I'm working through a paper on momentum in electrodynamics that requires the integration below and would greatly appreciate any help. I'm pretty sure it evaluates to $2/d$ but I can't quite figure ...
3
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0answers
45 views

The question about MTW 4-momentum integral expression and lorentz nature

In section 5.8 of Misner, Thorne, and Wheeler's "Gravitation" there is a proof that 4-momentum determined as $$ \tag 1 p^{\mu} = \int T^{\mu 0}\,\mathrm{d}^{3}\mathbf r , \quad \partial^{\mu}T_{\mu ...
1
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2answers
168 views

Is air drag equation in term of momentum still valid?

This is the known equation of air drag: $$m{\bf a}=mg-\mathcal D=mg-b{\bf v}.$$ Considering this, is air drag equation in term of momentum still valid? $$m{\bf v}=mv_g-b{\bf r}.$$
1
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1answer
141 views

Integration of constant: $\int dp = \Delta p$ in impulse formula

In University Physics, it has something like: $$\int \sum F dt = \int \frac{dp}{dt} dt = \int dp = \underbrace{p_2 - p_1}_{\Delta p?}$$ But I thought $\int dp = p$? Though my maths is really rusty ...