LITTLE MORE ON… MOMENT

LITTLE MORE ON… MOMENT BY GP CAPT NC CHATTOPADHYAY

MOMENT • Moment of force (often just moment) is the tendency of a force to twist or rotate an object;. This is an important, basic concept in engineering and physics. (Note: In mechanical and civil engineering, "moment" and "torque" have different meanings, while in physics they are synonyms. • Moment arm is a quantity used when calculating moments of force. • The Principle of moments is if an object is balanced then the sum of the clockwise moments about a pivot is equal to the sum of the anticlockwise moments about the same pivot. • A pure moment is a special type of moment of force. It is couple (mechanics). • Moment of a vector is a generalization of the moment of force. The moment M of a vector B about the point A is • MAB = rAB X B • Whererab is the vector from point A to the position where quantity B is applied. × represents the cross product of the vectors. Thus M can be referred to as "the moment M with respect to the axis that goes through the point A", or simply "the moment M around A". rAB B

INTERPRETATION • PHYSICAL: TURNING ACTION, ROTATION • GEOMETRICAL: AREA OF A TRIANGLE FORMED BY THE VERTICES OF FORCE VECTOR AND REFERENCE POINT F O A B F

Example B

Principle of moments • The Principle of Moments, also known as Varignon's theorem (not to be confused with the geometrical theorem of the same name) states that the sum of Moments due to several forces applied to a single point is equal to the Moment due to the sum (resultant) of the forces. Mathematically, this follows from: • (r x F1) + (r X F2) +… = r x (F1 +F2 +….)

PROOF • CLASS WORK

TORQUE • Torque, also called moment or moment of force, is the tendency of a force to rotate an object about an axis, fulcrum, or pivot. Just as a force is a push or a pull, a torque can be thought of as a twist. • Loosely speaking, torque is a measure of the turning force on an object such as a bolt or a flywheel. For example, pushing or pulling the handle of a wrench connected to a nut or bolt produces a torque (turning force) that loosens or tightens the nut or bolt. • The terminology for this concept is not straightforward: In the US, in physics it is usually called "torque" and in mechanical engineering it is called "moment” However outside the US this varies. In the UK for instance, most physicists will use the term "moment". In mechanical engineering, the term "torque" means something different described below. ". • The symbol for torque is typically τ, the Greek lettertau. When it is called moment, it is commonly denoted M.

TORQE DEFINITION CONTD…… • The magnitude of torque depends on three quantities: First, the force applied; second, the length of the lever armconnecting the axis to the point of force application; and third, the angle between the two. • In symbols: τ =r X F where τ is the torque vector and τ is the magnitude of the torque, r is the displacement vector (a vector from the point from which torque is measured to the point where force is applied), and r is the length (or magnitude) of the lever arm vector, F is the force vector, and F is the magnitude of the force, × denotes the cross product, θ is the angle between the force vector and the lever arm vector. The length of the lever arm is particularly important; choosing this length appropriately lies behind the operation of levers, pulleys, gears, and most other simple machines involving a mechanical advantage. • The SI unit for torque is the newtonmetre (N·m). For more on the units of torque, see below.

Torque vs moment • In mechanical engineering (unlike physics), the terms "torque" and "moment" are not interchangeable. "Moment" is the general term for the tendency of one or more applied forces to rotate an object about an axis (the concept which in physics is called torque) • "Torque" is a special case of this: If the applied force vectors add to zero (i.e., their "resultant" is zero), then the forces are called a "couple" and their moment is called a "torque” • For example, a rotational force down a shaft, such as a turning screw-driver, forms a couple, so the resulting moment is called a "torque". By contrast, a lateral force on a beam produces a moment (called a bending moment), but since the net force is nonzero, this bending moment is not called a "torque". • TORQUE (T= I. α ) OF A ROTARY MOTION WILL BE STUDIED LATER.

TORQUE VS ANGULAR MOMENTUM • Relationship between forceF, torque τ, linear momentump, and angular momentumL in a system which has rotation constrained in one plane only (forces and moments due to gravity and friction not considered

LEVERS • SIMPLE MECHANICAL DEVICE TO GAIN MECHANICAL ADVANTAGE P X a = W X b b a P W MECH ADV = W/P = ( a/b) IN A COMPOUND LEVER THE M.A OF EACH LEVER IS MULTIPLIED, SO, M.A COMPOUND = ∏(ai / bi)

LET’S HAMMER…. THE BRAIN

NUMERICAL • As per class work

LET ME GO THROUGH…. • NOW I GO THROUGH THE BOOK…. OSMANY HALL ENGINERING MECHANICS

LITTLE MORE ON… MOMENT