Force, Moment of Force, and Equilibrium

Flashcards covering the fundamentals of force, translational and rotational motion, torque, couples, and the principles of equilibrium based on the lecture notes.

Force

A quantitative measure defined as the rate of change in linear momentum ($F = \frac{dp}{dt}$), which in S.I. is measured in newton ($N$) and in gravitational units as kilogram-force ($kgf$).

Linear or translational motion

The motion produced when a force acts on a stationary rigid body free to move, causing it to move in a straight path in the direction of the applied force.

Rotational motion

The turning effect of a force on a body pivoted at a point, causing it to rotate about an axis passing through the pivoted point.

Moment of a force (Torque)

The product of the magnitude of the force ($F$) and the perpendicular distance ($OP$) of the line of action of the force from the axis of rotation ($\text{Moment of force} = F \times OP$).

Anticlockwise moment

The turning effect that rotates a body in an anticlockwise direction, conventionally taken as positive ($+$).

Clockwise moment

The turning effect that rotates a body in a clockwise direction, conventionally taken as negative ($-$).

$$1\,kgf$$

A gravitational unit of force equal to the force exerted by gravity on a $1\,kg$ mass, specifically $1\,kgf = 9.8\,N$ (average on Earth).

$1\,N\,m$ in C.G.S. units

The S.I. unit of moment of force expressed in C.G.S. as $10^7\,dyne\,cm$ ($10^5\,dyne \times 10^2\,cm$).

Couple

A pair of equal and opposite parallel forces that do not act along the same line, which is required to produce rotation.

Couple arm

The perpendicular distance ($d$) between the two equal and opposite forces that constitute a couple.

Moment of couple

The product of either force ($F$) and the perpendicular distance between the two forces ($d$), expressed as $F \times d$.

Equilibrium

A state where a number of forces acting on a body produce no change in its state of rest or of linear or rotational motion.

Static equilibrium

The condition in which a body remains at rest despite being influenced by several forces, such as a book lying on a table.

Dynamic equilibrium

The condition in which a body remains in the same state of translational or rotational motion under the influence of several forces, such as a rain drop falling with constant velocity.

Principle of Moments

The rule stating that for a body in equilibrium, the algebraic sum of the moments of all forces about the axis of rotation is zero ($\text{sum of anticlockwise moments} = \text{sum of clockwise moments}$).

Conditions for equilibrium

1. The resultant of all forces acting on the body must be zero. 2. The algebraic sum of moments of all forces about the point of rotation must be zero.

Newton-metre ($N\,m$) vs. Joule ($J$)

While both share the same base units, $N\,m$ is used for torque (a vector), whereas $J$ is reserved for work or energy (scalar quantities).