Consider taking off on an airplane, now riding a merry-go-round. And finally, going down and lift. On the airplane, we'll fill us if you're being pushed backwards into your seat. On a merry-go-round, you'd fill us if you're being pushed outwards. On the lifts, you'd fill us if you're floating. Now what do all these events have in common? Well, it turns out that all these forces pushing us up, down or outwards are actually not real. They only appear to act on objects, or in this case us. We call them Fixitious Forces. A Fixitious Force is an apparent force that acts upon all masses whose motion is described using a non-inertial frame of reference. An inertial frame is one where there is direct acceleration, so either remain stationary or move that constant velocity. Newton's laws of motion apply, for example an airport. A non-inertial reference frame moves in a non-uniform or accelerated motion, so when the plane leaves the runway, it is accelerating, so it is a non-inertial reference frame. Here Newton's laws of motion do not apply. Fixitious forces are introduced so that Newton's second law is valid in a non-inertial frame. Imagine that Mario is standing on a plane, which is taking off with an acceleration A. He feels the force pushing him backwards. Due to the reference frame's motion, it appears that Mario is being pushed in the direction opposite to acceleration of the plane. This is called the Translation of Fixitious Force. The second Fixitious Force is called the centrifugal force. Imagine Mario is standing on a merry-go-round, which is spinning with an angular velocity omega. To an inertial observer on the ground, it is easy to see that to keep Mario in his rotational motion, a continuous centripetal force must be applied perpendicular to his direction of motion. This is equal to M v squared over R. This force will be pushing Mario radially inwards. Now, from Mario's point of view of the rotating non-inertial frame, he feels an apparent force pushing him outwards. This is called the centrifugal force, and will be equal in modulus and opposite in direction with respect to the centripetal force. We also know that the velocity v is equal to the angular velocity omega multiplied by the radius, so we can rewrite the centrifugal force as M R omega squared. To explain the cruelest force, we first need to introduce a new vector. So imagine a merry-go-round, this spinning with an angular velocity omega. We introduce a vector perpendicular to the plane of rotation, represented by a capital omega, called angular velocity vector. Imagine Mario is running across the merry-go-round with a velocity v. There will be a fictitious force, the cruelest force acting on him, which is given by an active M times v cross omega. We'll need to use the right hand rule because of the cross-product. The next tip sign in the equation means that the cruelest force is pointing in the opposite direction. So in this case, the cruelest force will be pointing inwards. The last fictitious force is called the u-the-force or as a muthophores. Imagine Mario is standing on the merry-go-round with a distance R from the center, and someone is pushing him. This will cause a change in angular velocity. We can express this as a vector d omega dt. The fictitious u-the-force acting on him is given by negative M d omega dt cross R. In this case, the cross-product will give vector-cushing Mario inwards. If a person in an accelerating non-inertial reference string wanted to find their acceleration, then we need to add up all the real and fictitious forces together. This is the form that Newton's second law takes in non-inertial frames. Fictitious forces are present in our everyday lives. We've just grown so used to them that we've very noticed them anymore. Now remember, the pseudo-force that is felt during acceleration can also be felt during deceleration only in the other direction. So next time you get in a car, put on your seatbelt. The force from your forward during crash might be fictitious, but the impact will be real.