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Uniformly accelerated motion; angular momentum definition

Short answer

Straight-line motion with constant acceleration a: v = u + at, s = ut + ½at², v² = u² + 2as. Angular momentum of a particle about O is H_O = r × mv; its rate of change dH_O/dt = ΣM_O, the sum of moments of forces about O.

What is uniformly accelerated rectilinear motion? Also define the angular momentum and its rate of change.

Uniformly accelerated rectilinear motion

Straight-line motion with constant acceleration a. The governing equations (u = initial velocity, v = final velocity, s = displacement, t = time) are:

  • v = u + at
  • s = ut + ½at²
  • v² = u² + 2as

Example: a body in free fall (a = g = 9.81 m/s²).

Angular momentum and its rate of change

The angular momentum of a particle of mass m and velocity v about a point O is the moment of its linear momentum about O:

H_O = r × mv

Its magnitude is H_O = m v r sin φ (SI unit kg·m²/s). For planar motion in polar coordinates, H_O = m r² θ̇.

Its rate of change equals the moment of the resultant force about the same point: dH_O/dt = r × F = ΣM_O. If the moment of the force about O is zero (for example a central force), angular momentum is conserved.

✓ Answer checked by Claude Opus 5.5 (high effort)

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