---
title: "Uniformly accelerated motion; angular momentum definition"
subject: "Applied Mechanics"
chapter: 8
key: "semester_1/applied_mechanics:uniformly-accelerated-motion-angular-momentum"
source: https://www.bctengineer.com/q/semester_1/applied_mechanics/uniformly-accelerated-motion-angular-momentum
site: BCT Engineering
---

# Uniformly accelerated motion; angular momentum definition

Applied Mechanics · Chapter 8: Kinematics of Particles and Rigid Body

- Asked in: 2071 Chaitra, 2+2 marks
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_1/applied_mechanics/uniformly-accelerated-motion-angular-momentum
- Whole chapter: https://www.bctengineer.com/md/semester_1/applied_mechanics/chapter-8

## Question

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

## 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.

## Answer

#### 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.

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Which is a valid equation for uniformly accelerated rectilinear motion?
   A. v = u + at^2
   B. s = ut + 1/2 at^2
   C. v^2 = u^2 + as
   D. s = vt^2
   Answer: B. The three equations are v = u + at, s = ut + 1/2 at^2 and v^2 = u^2 + 2as. (Key point: Uniform acceleration)

2. What is the angular momentum of a particle about O?
   A. Its linear momentum mv
   B. The moment of its linear momentum about O: H_O = r x mv
   C. The moment of the force about O
   D. m r omega only for circles
   Answer: B. H_O = r x mv with magnitude m v r sin φ. (Key point: Angular momentum definition)

3. What does dH_O/dt equal?
   A. The force F
   B. The moment of the resultant force about O (ΣM_O)
   C. Zero always
   D. Kinetic energy
   Answer: B. dH_O/dt = r x F = ΣM_O; when the moment is zero (central force) H_O is conserved. (Key point: Rate of change)

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