By definition of the fundamental units, this yields 1 lbf = 1 slug Г— ft/s 2, or 1 lbf = 32.174 lbm Г— ft/s 2. This is obtained by utilizing NewtonвЂ™s second law with gravitational acceleration, i.e. It is not proper to say that 1.00 kg equals 9.81 N, but it is proper to say that 1.00 kg weighs 9.81 N under standard earth gravity. To the right, since F x is the x-component of vector F, and a x is the x-component of acceleration vector a. How much force (in Newtons) is required to accelerate a mass of 13.3 kg at a constant acceleration of 1.20 m/s 2? Thus it is the conversion factor with which to multiply or divide any equation to simplify the units. The above expression is dimensionless and has a value of 1. By definition of the fundamental units, this yields 1 N = 1 kg Г— m/s 2. The following is provided to avoid confusion, especially with English units. The relationship between force, mass, and acceleration can be clearly understood with NewtonвЂ™s second law.The relationship between force and mass units.The following is an attempt to clarify some of this confusion: The use of g c has complicated and further confused the issue, in this authorвЂ™s opinion. There has been much confusion (and numerical error!) because of the differences between lbf, lbm, and slug.Instead, NewtonвЂ™s law should remain in the fundamental form in which it was created, without an artificial constant thrown into the equation, simply for unitвЂ™s sake. The present author discourages use of this constant, since it leads to much confusion.I.e., instead of F = m Г— a, they write F = m Г— a/g c, where g c is defined in the English Engineering System of Units as Some authors define a gravitational conversion constant, g c, which is inserted into NewtonвЂ™s second law of motion.Comment about the gravitational conversion constant, g c.There are conversion factors listed in many textbooks to enable conversion from any of these units to any other. Note that there are many other units, both metric and English, in use today.ДЇor example, power is often expressed in units of Btu/hr, Btu/s, cal/s, ergs/s, or horsepower, in addition to the standard units of watt and ft Г— lbf/s.These are called secondary dimensions, with their corresponding secondary units.ДЄ few examples are given in the table below: All other dimensions can be derived as combinations of these seven primary dimensions.These are listed in the table below for the three unit systems: In order to assign numbers to these primary dimensions, primary units must be assigned.The others will not be of concern to most mechanical engineering analyses. Only the first four of these are required. The primary dimensions are: mass, length, time, temperature, electric current,ДЇor most mechanical and thermal science analyses, however,.Primary (sometimes called basic) dimensions are defined as independent or fundamental dimensions, from which other dimensions can be obtained. In total, there are seven primary dimensions.The latter two are similar, except for the choice of primary mass unit and use of the degree symbol, as discussed below.the British Gravitational System of Units (BG).the English Engineering System of Units (commonly called English units).the International System of Units (SI units, from Le Systeme International dвЂ™Unites, more commonly simply called metric units).There are three primary unit systems in use today:.For example, length is a dimension, but it is measured in units of feet (ft) or meters (m).

There is a difference between dimensions and units.ДЄ dimension is a measure of a physical variable (without numerical values), while a unit is a way to assign a number or measurement to that dimension.

Since our expectation is that some amount of energy is needed to raise the temperature of water, we can be more confident in the answer.Dimensions, Units, Conversion Factors, and Significant Digits

As others have pointed out, Nm and N/m are very different, as are $Nsm^$). One thing that is important to note is the importance of dimensional analysis. As the Wiki page puts it: When prefixes are used to form multiples and submultiples of SI base and derived units, the resulting units are no longer coherent. But, if you mix and match prefixes in a unit (gram per cubic centimeter, for example), then you've fallen off the SI truck. When you see a measurement expressed purely in terms of one or more of those units (like Nm or N/m), then it is an acceptable SI unit. There are a bunch of derived units and acceptable prefixes (for orders of magnitude) (see that Wikipedia page). There are seven fundamental SI units (seconds (time), metres (length), kilograms (mass), ampere (current), kelvin (temperature), mole (amount of substance) and candela (luminous intensity).

Newton units