A Force with a Lot of Inertia
You may not think so, but I bet you can tell the difference between inertial force and gravitational force. After all, you use forces all day long! Even during sleep!
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Okay, so what's the big deal?
I hate to force the issue, but the big deal is that force is truly a big force in our lives. We use forces a hundred times a day. In fact, we use both linear and rotational forces continually, and we always have to put up with a lot of gravity. (Remember gravity?)
From Newton we know the earth pulls down on objects and tends to make them fall. But they don't just fall -- they fall in a special way, by increasing their speed. They accelerate. This according to Newton's theory. (Einstein's Relativity theory came later and more or less took over, but still reduces to the Newtonian version when object speeds are low and the speed of light can be considered to be infinite. You can also say that Quantum Mechanics superceded Relativity Theory, but that's a whole different story. See here.)
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When talking about forces, we distinguish between gravitational and non-gravitational forces.
Inertial forces are the non-gravitational kind, which means they aren't produced by an attraction with the earth -- or with any other gravity system. These are forces we ourselves can produce, and do produce in great abundance. They have a lot to do with empowerment.
When it comes to inertial forces, too, we have in mind either linear (straight-line) forces or rotational (circular) forces. In other words, there are two kinds of inertial force. One is plain vanilla inertial force and the other is torque, or what's called moment of force. The difference between them depends on whether the force produces linear motion or rotational motion.
By virtue of acceleration, we can talk about forces acting on an object. This step from speed to acceleration provides the basis for dynamics. More technically, the consequence of an unbalanced force (a non-zero net force) acting on a body is that the body accelerates.
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If you're not already going around in circles, linear motion is straight-line motion. To keep things straight, rotational motion means going around in circles. Got it?
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You probably already guessed that linear force is a force applied along a straight line.
A body moving with a constant velocity has momentum (which is mass (m) times speed (v), or mv), but it doesn't have acceleration. So it gives no sign of an unbalanced force. If forces are actually applied in such a case, they necessarily cancel each other out -- their net effect is zero.
According to the first principle of mechanics (as proposed by Newton), an object will remain at rest or in a state of constant motion in a straight line provided no unbalanced force acts on the object. This is a basic principle of inertia. It says, in effect, that force is needed to overcome inertia (or momentum) to change an object's speed or direction.
To determine the amount of force needed to speed up an object or slow it down by some amount, Newton offered his second law: The unbalanced force, F, is the product of the inertial mass, m, and the acceleration, a. That is,
F = ma
The greater the mass, or inertia, the greater the force required to generate a given amount of acceleration. And the greater the acceleration exhibited by the body, the greater the force being applied. In other words, force is proportional to the mass (weight), and proportional to the acceleration.
If you compare the expression for force with that for momentum, you will see that one involves acceleration and the other involves velocity. In fact, force can be defined as the rate of change of momentum. That's the way Newton originally expressed it.
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Rotational force (or torque) is a force that tends to rotate an object, either about its center of mass, if it is spinning freely, or about some fixed axis, like a hinge about which a door is swung. When you open a door, you apply torque. A torque shouldn't be confused with simple force. As a moment of force -- a lever -- it's a twisting action. That is, torque measures the rotational effect of a force. When you open a door, you "twist" it around its hinges.
Whereas force acts against inertial mass to change the linear velocity of an object, torque acts against the moment of inertia of an object to change its angular velocity. That is, torque produces angular acceleration. (When you hear 'moment of ...', just think of a lever, of twisting.)
Following what we did with force, we can define torque as the product of the moment of inertia and angular acceleration, or
T = Ia
where T is the torque, I is the moment of inertia and a is the angular acceleration.
Comparing torque and angular momentum, you can see that the former involves angular acceleration and the latter involves angular velocity. Torque can then be defined as the rate of change of angular momentum.
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