Topic 3 ( MOMENT OF A FORCE AND COUPLE ) Flashcards
describes its rotational effect about a point or axis. It is a critical concept in mechanics, widely used to analyze and design structures and mechanical systems.
moment of a force
he product of a force and the perpendicular distance (moment arm) from the force’s line of action to the point of rotation.
moment of a force
Definition: The total moment about a point equals the sum of the moments of the individual force components.
Significance: Simplifies the calculation of moments in complex force systems.
Principle of Moments (Varignon’s Theorem)
Definition: A pair of equal and opposite forces separated by a distance, creating a pure rotational effect with no net translational force.
Couple
reveal how forces cause objects to rotate, which is crucial for ensuring stability in structures and mechanisms.
Moments
By breaking forces into components, complex systems become easier to analyze, saving time in engineering calculations
Varignon’s Theorem
produce rotation without translation, making them essential in designing gears, levers, and other mechanical systems.
Couples
is a measure of the tendency of a force to cause an object to rotate about a specific point or axis. Think of it as the “rotational effect” of a force.
moment
in statics is a pair of forces that are equal in magnitude, opposite in direction, and act along different lines of action.
couple
You push the wheel up with one hand and pull it down with the other.
The forces your hands apply are equal in strength (magnitude) but point in opposite directions.
These forces create a turning or rotational effect that makes the wheel spin.
This is an example of a ____ The forces work together to produce rotation without moving the wheel sideways or forward.
couple!
When you push it straight ahead, it slides forward without flipping or turning.
This is a_____ because the car moves in a straight line from one place to another.
translation
The______ refers to the linear movement of an object when forces act on it. In simpler terms, it’s when a force causes an object to move straight from one point to another without rotating. This movement can happen in any direction—left, right, up, down, or diagonally.
translational effect
is about a point is the tendency of the applied force to rotate a body about a reference point
moment of a force
As the magnitude of the force tends to move the body in the direction of the force, called a ___
translational effect,
is defined as the product of the magnitude of the force times the perpendicular distance from the line of action of the force to the point, that is,
The moment of a force
Where d is the perpendicular distance is called the
moment arm
If the line of action of the force passes through the point, the moment is equal to what?
zero,
A______is the turning effect of a force about a point or axis.
Moment
M=F⋅d, where
𝐹
F is force and
𝑑
d is the perpendicular distance to the point of rotation.
Moment
Created by a single force acting at a distance from a pivot point.
Causes rotation or turning about a point or axis.
A single force or a system of forces can cause a moment.
Moment
A ______can cause both translation and rotation depending on the system.
EX. Opening a door by applying force at the handle.
A seesaw on a playground.
Moment
A _____is a system of two equal and opposite forces whose lines of action do not coincide.
Couple
Created by two forces of equal magnitude but opposite direction, separated by a distance.
Causes pure rotation without translation.
Always involves two equal and opposite forces.
Couple
M=F⋅d, where
𝑑
d is the perpendicular distance between the forces (arm of the couple).
Couple
A couple causes only rotation, no translation.
Ex. Turning a steering wheel using both hands.
Tightening a bolt using a wrench.
Couple
refers to the movement of an object in a straight line or along a path where every point of the object moves the same distance and in the same direction. Essentially, the object does not rotate or twist; it simply shifts from one position to another.
Translation
Every part of the object moves in the same direction and distance.
Translation:
The object spins about an axis, and different points move in circular paths.
Rotation:
