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Why does a coin placed on the card drop on the tumbler when the card is rapidly flicked with the finger?

Answer
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Hint: We know that according to Newton, his first law of motion asserts that if a body is at rest or moving in a straight line at a constant speed, it will stay at rest or continue to move in a straight path at a constant speed unless it is acted upon by a force. The law of inertia is the name given to this proposition.

Complete answer:
We know that if we continue to move in any direction a force is required either to stop or to increase the speed or to change the direction of our motion. Here, in the case of card and the coin the reason for this is that when the card is flipped, it experiences a transient force that causes it to move away. However, due to inertia of rest, the coin kept on it does not share the motion at the same time and remains motionless at its location. The coin then falls into the tumbler due to gravity's pull.

Note: So, we have to remember that the coin is at rest due to the inertia and it finally falls due to the gravitational force acting on the coin which acts on it when it is free to fall down into the tumbler. We know that the gravitational force is a kind of attractive force which always tends to pull the objects toward itself.