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ModPhy1/Unit1/Special Relativity/Inertial Frame/Non-Inertial Frame/ |
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Fictitious Forces |
Fictitious Forces are imaginary forces that result from treating a non-inertial
frame as if it were inertial.
When an observer is in a non-inertial frame but perceives himself as being in a normal, inertial frame, he notices that free bodies do not move as expected, namely, in a straight line at a constant speed. Objects released at rest will accelerate and objects in motion will deviate from a straight line. Therefore, the observer intuitively concludes that some mysterious unknown force must be pushing on the objects.
We even give names to these forces. We say that inertia, or an inertial force, makes people lunge forward in their seats when a car decelerates rapidly to a stop. A centrifugal force makes a rock fly outward when it is slung in a circle at the end of a string. A Coriolis force makes the wind change directions as it blows across the surface of a rotating earth.
But these forces are not real. They do not result from the interaction
between two physical objects. They do not obey
If inertia were really pushing people forward when a car stops, then the people would be pulling backward on inertia. But search as you will, you will never find an object named inertia either in front of the people pulling them forward or in back pushing them forward. Similarly, there is no physical object pulling a rock outward when slung in a circle or pushing the air sideways as it blows over the earth.
Another characteristic of fictitious forces that distinguishes them from real forces is that they are always proportional to the mass of the object being accelerated. Therefore, they can always be eliminated by viewing the situation from a different frame of reference. Since they are a direct consequence of viewing things from a non-inertial frame, they can be eliminated simply by viewing things from an inertial frame.
For example, there is nothing pushing people forward when a car decelerates rapidly to a stop. They simply continue moving forward in a straight line with a constant speed just like they have always been doing. It is the car that is being pushed, not the people. The car is thrust backward, not the people forward. And the force pushing on the car is a real force of interaction between two physical objects. It is the friction force (electromagnetic) between the tires and the pavement.
Similarly, there is no force pulling the rock outward when it moves in a circle. The rock is simply trying to continue moving in a straight line at constant speed. It is the tension in the string, a real (electromagnetic) force, that pulls the rock away from the inertial straight line and into the circle.
And finally, even though the wind naturally blows along a curved path on the rotating earth, it actually travels along a straight line when viewed from a non-rotating frame.
Because the force of gravity on an object is proportional to the mass of the object, it behaves exactly like a fictitious force. And like all fictitious forces, it can be eliminated simply by viewing the situation from another frame of reference. In the case of gravity this frame is one that falls freely with the object. That is why people feel weightless in a falling elevator, in NASA’s “vomit comet,” or in a spaceship orbiting the earth.
Q1. Merry-go-round.
Three children are playing catch on a playground merry-go-round. One of them is
standing on the ground pushing the platform so it rotates with constant speed.
The other two are sitting on opposite sides of the rotating platform tossing a
ball back and forth. When the third child is passing through his northernmost
position moving west he throws the ball so as to be caught by the second child
directly south at that time. Ignoring any vertical motion of the ball, in what
direction and at what speed should he throw the ball? (A)
Directly south at any speed. (B) Southeast slower than
his own speed over the ground. (C) Southeast faster
than his own speed. (D) Southwest faster than his own
speed. (E) East faster than his own speed.
Q2. In classical
physics, which of the following are classified as fictitious forces? (A)
Gravitational force, (B) Coriolis force, (C) Centrifugal force. (D) Two of
these. (E) Three of these.
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ModPhy1/Unit1/Special Relativity/Inertial Frame/Non-Inertial Frame/