When speaking of the effects of force on mass in the phenomenon of inertia, it can be easy to accidentally refer to force as "inertial force." This can probably be traced back to the terms "force" and "inertial mass." Force is an amount of energy that causes an object to change speed, direction or shape, while inertial mass is a measure of how resistant an object is to changing its state of motion when that force is applied. In this instance, it is assumed that "inertial force" refers to the amount of force it would take to move a certain object or stop it from moving entirely. This can be found using Newton's second law -- F = ma -- which translates to, "Force equals inertial mass times acceleration."
Keep in mind that acceleration is traditionally measured in meters per second per second, or meters per second squared. The standard rate of miles per hour was substituted to make the example more understandable.
Find the mass of the object that you wish to calculate the starting or stopping force for. On the earth's surface, the mass of an object is roughly equal to its weight in kilograms, so you can find the mass by simply weighing the object on a scale. If the object is in motion, you may need to know the weight/mass of the object beforehand.
Find the object's rate of acceleration. If you are trying to gauge the inertial force of a moving object (a car, for example) and its rate of acceleration is unknown to you, you will need a speedometer to find its rate of acceleration. You can do this by measuring the speed of the object at one point in time and then measuring it again a few seconds later. This is because acceleration is the measure of how fast an object is increasing its speed over time.
Mark the times at which you measured the object's speed. Subtract the first speed from the second speed. Then divide the result by the amount of time between the two measures. If you measure a car rolling at 40 mph at 1:00 p.m. and then measure it at 41 mph a minute later, you can say that the rate of acceleration is (41 mph - 40 mph) divided by 1/60h. This gives us 1 mph divided by 1/60h, or an acceleration of about 59 mph per hour. This means that, if the car maintained its current rate of acceleration, its speed would increase by 59 miles every hour. Keep in mind that this equation assumes that the car is accelerating at a constant rate and doesn't take outside variables, such as gravity or friction, into account.
Multiply the object's mass by its acceleration. This will give you its inertial force. In the case of the car, we will assume its mass is about 1,000 kilograms. If it maintains its current rate of acceleration, it would require approximately 59,000 kg (about 65 tons) of counter-force to stop it instantaneously. The amount of inertial force required to stop a moving object will be exactly equal to the amount of inertial force that set it into motion in the first place. This is why a small object that is moving very quickly (such as a bullet) and a large object that is moving very slowly (such as a boulder) are both equally destructive and difficult to stop without the proper amount of counter-force. If the object is not moving, the amount of inertial force required to move it is generally equal to the mass of the object.
- "How Everything Works: Making Physics Out of the Ordinary";,Bloomfield, Louis; John Wiley & Sons (2007),