Units of Measurement and Conversion Factors

Clearly understanding the units of measurement is very important, but seldom given enough attention because the beginning student is usually hurried along through other topics.

Mass is the quantity of matter in the thing you are studying. The metric unit of measurement of mass is the kilogram (kg), which is 1000 grams. The English unit is the slug, which is rarely used. The mass center of an object is where the balance point is.

Weight is a force, which arises when a mass is acted on by gravity. The metric unit of weight should technically be the Newton (N), which is the unit of force, but commonly it is the kilogram of mass that is used to measure weight in the metric system because gravity is about the same everywhere on the Earth. The English unit of weight is the pound (lb).

Length in the metric system is measured by meters (m), and in the English system by feet (ft). A mile is 5280 feet or 1609 meters (1.6 kilometers).

Velocity is how fast something is moving in a certain direction. Remember, direction is key. You can have negative velocity if you are moving in the wrong direction. In the metric system, the unit for velocity is meters per second (m/s). In the English system, it miles per hour (mph).

Momentum is when a mass has a velocity. The unit has no name in the metric or the English system, but it is kg.m/s (mass times meters per second). Note that mass is just as important as speed in calculating momentum, and also note that momentum has a direction. Momentum is conserved in any collision, which means that you add the momenta of the two colliding objects (remembering that velocity can be negative) and the sum of their momenta after the collision must be the same, no matter if they are made of clay or diamond. Conservation of Linear Momentum and Conservation of Angular Momentum are key concepts in elementary mechanics.

Acceleration is the rate of change of velocity: meters per second, per second (m/s²). In the English system, it is feet per second, per second.

Force is when you have a mass being accelerated or decelerated (Newton’s Second Law: F = ma) in a certain direction. Because force always has a magnitude (how much) and a direction, it is represented by an arrow (called a vector). The unit of measurement of force in the metric system is the Newton, which is kilograms times meters per second per second (kg.m/s²). In the English system, force is measured in pounds (lbf). The metric unit is much superior for clear understanding of the concept of force, which is frequently confused with energy and momentum. Be sure you know exactly what the difference is. Also, study the difference between force and torque.

Energy, work, and heat are all measured in the metric unit of the joule, which is kg.m²/s² — you can see that this is Newtons times meters. This unit represents the result of a force moving something a distance, such an accelerating racquet, impelled by the force of the player’s muscles contracting (especially the belly muscles), moving to hit a serve. There is a confusing multitude of measurement units in the English system because these units arose before thermodynamics evolved as a science using the fact that energy, work, and heat were all the same thing, and could be interchanged to produce engines. In the English system, the unit of measurement of heat is the Btu (British thermal unit) which is equivalent to 1055 joules. There is also another unit of measurement called the calorie which is used for heat or energy, and is equivalent to 4.186 joules. The calorie used for describing food is actually 1000 calories, and is written with a big C. For work, the English system uses the foot pound (ft.lbf), which is the amount of work or energy used to lift an object weighing one pound a distance of one foot. Energy is also conserved, like momentum, but it shifts forms, unlike momentum, between kinetic energy (the energy of a moving object), to potential energy (the energy that is stored in an object), to internal energy (heat), to work. How much energy is lost in a collision, by being converted to forms other than kinetic energy, is measured by the Coefficient of Restitution (COR). This is the bounce, or more technically, elasticity, and can never be greater than 1.

Torque is a twisting force, and the twist occurs because the force is not applied to the object’s mass center so as to be a push. When you put spin on the ball, you impart a torque to it. The impact of the ball imparts a torque to your racquet. The metric unit of measurement is the Newton meter (N.m), which is a force times the distance this force is from an axis of rotation. The English unit is foot pounds or pound feet.

Power is the rate of doing work, and is measured in the metric unit of the watt (W), which is one joule per second. A kilowatt (kW) is a thousand watts. The English unit is the horsepower (hp), which is equivalent to 746 watts, or 2545 Btu per hour, or 550 foot pounds per second. If you weigh 100 pounds and can climb 11 feet of rope in two seconds, you have one horsepower, which is strong. Be sure you understand the difference between power, energy, force, and momentum.

Conversion factors
1 mile per hour = 0.447 m/s 1 meter per second = 2.237 mph
1 Newton of force = 0.2248 lb. 1 pound = 4.4484 N
1 centimeter = 0.3937 in. 1 inch = 2.5400 cm
1 kilogram of mass = 35.28 oz. 1 ounce = 28.35 grams
1 joule of energy = 0.7376 ft.lb 1 foot pound = effort to lift a pound a foot = 1.3557 J
1 Newton.meter of torque = 0.7376 lb.ft 1 pound foot (foot pound) = 1.3558 N.m