understanding units-torque & power

8/4/2019 Understanding Units-Torque & Power

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FORCE

In physics, a force is any influence that causes a free body to undergo a change in speed, a change in

direction, or a change in shape. Force can also be described by intuitive concepts such as a push or

pull that can cause an object with mass to change its velocity (which includes to begin moving from a

state of rest), i.e., to accelerate, or which can cause a flexible object to deform. A force has both

magnitude and direction, making it a vector quantity. Newton's second law, F=ma, can be

formulated to state that an object with a constant mass will accelerate in proportion to the net force

acting upon and in inverse proportion to its mass, an approximation which breaks down near the

speed of light. Newton's original formulation is exact, and does not break down: this version states

that the net force acting upon an object is equal to the rate at which its momentum changes.

ForceSI symbol: F

SI unit:newton

Derivations from other quantities: F = m a

WORK

In physics,mechanical work is the amount ofenergy transferred by a force acting through a distance

in the direction of the force. Like energy, it is a scalar quantity, with

SI units ofjoules.

Ifa force F that is constant with respect to time acts on an object while the object is displaced

in a straight line along the length and direction ofa vectord, the mechanical work done by

the force on the object is the dot product of the vectorsF and d:[4]

Ifthe force and the displacement are parallel and in the same direction ( = 0), the

mechanical work is positive.

TORQUE

Torque, also called moment ormoment of force (see the terminology below), is the

tendency ofa force to rotate an object about an axis,[1]

fulcrum, or pivot. Just as a force is apush or a pull, a torque can be thought ofas 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 ofa wrench connected to a nut or bolt

produces a torque (turning force) that loosens or tightens the nut or bolt.


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The terminology for this concept is not straightforward: In the US, inphysics it is usuallycalled "torque" and in mechanical engineeringit is called "moment".

[2]However outside the

US this varies. In the UKfor instance, most physicists will use the term "moment". Inmechanical engineering, the term "torque" means somethingdifferent,[3] describedbelow. In

this article the word "torque" is always used to mean the same as "moment".

The symbol for torque is typically , the Greek lettertau. When it is called moment, it iscommonly denotedM.

The magnitude of torque depends on three quantities: theforce applied, the length of the lever

arm[4]

connecting the axis to the point offorce application, and the angle between the forcevector and the lever arm. In symbols:

where

is the torque vector and is the magnitude of the torque,

r is the displacement vector (a vectorfrom the point from which torque is measured tothe point where force is applied), and ris 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, 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 oflevers,pulleys, gears, and most othersimple machines involving a

mechanical advantage.

The SI unitfor torque is the newton metre (Nm).

One newton metre is equal to the torque resulting from a force of one newton applied

perpendicularly to a moment arm which is one metre long.

y 1 newton metre = 0.7375621 foot-pound force (often "foot-pound")

y 1 kilogram-force metre = 9.80665 Nm[5][6]

y 1 foot-pound force (often "foot-pounds") = 1pound-forcefoot (often "pound-foot")

1.3558 Nm

TORQUE CARTorque is the amount of "turning power" you have, much in the same way you turn a wrench. 369

foot-pounds means that if you had a wrench that was 1 foot long, and applied a force of 369 pounds

directly perpendicular to that wrench, you would get 369 foot-pounds of torque

Well, what can this do to a car? The answer is: cause it to accelerate! The torque

specification they give is the maximum torque of the internal-combustion engine, which isusually a higher value than the actual torque on the wheels. (Seewikipediafor more details.)


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But this torque can tell you a lot about how fast the car can accelerate. Let's turn it into aphysics problem. We'll assume that this "500 Newton-meters" is an actual, legit value for

how much torque the tires experience. We can estimate that the mass ofa typical car is about1500 kg, and that the typical distance between the center of mass of the car and the wheel's

rotational axis is about 20 cm; this gives us a moment of inertiafor the car of60 kg m^2. Thecar's wheel sizeplus the sidewall radius of the tire is about 20", or 51 cm.

The acceleration of this car? 4.25 m/s^2, or (more commonly), it can do 0-60 miles-per-hour

in about 6.3 seconds. Want a car that can accelerate faster? Here are the things that can help:

y more torque (duh),y a lighter car,y a lower center-of-mass (closer to the wheel axle in height),y larger diameter wheels & tires,y and an engine that can output this large amount of torque over a wide range of engine

speeds.

POWER

Inphysics, power is the rate at which workis performed orenergy is converted.[1][2] As a

simple example, burning a kilogram ofcoal releases much more energy than does detonatinga kilogram ofTNT,[3] but because the TNT reaction releases energy much more quickly, it

delivers far more power than the coal. IfW is the amount ofworkperformed during aperiod oftime ofduration t, the average powerPavg over that period is given by the

formula

It is the average amount ofwork done or energy converted per unit of time. The average

power is often simply called "power" when the context makes it clear.

The dimension of power is energy divided by time.

The unit of power is the watt (W), which is equal to onejoule per second.Other units of power

include horsepower (hp), metric horsepower (Pferdestrke (PS) or cheval vapeur, CV), and foot-

pounds per minute. One horsepower is equivalent to 33,000 foot-pounds per minute, or the power

required to lift 550 pounds by one foot in one second, and is equivalent to about 746 watts.

understanding units-torque & power

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