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Frames: inertial vs non-inertial
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Newton's laws hold in inertial frames; fictitious forces appear otherwise.
An inertial frame moves at constant velocity; Newton's laws hold in it. An accelerating or rotating frame is non-inertial, and extra fictitious forces (centrifugal, Coriolis, −ma) appear.
In a braking bus you are thrown forward: from the ground there's no force, only inertia.
Don't add fictitious forces when working in an inertial frame.
In more detail
An inertial frame moves at constant velocity and feels no fictitious forces. A non-inertial frame, such as one that accelerates or rotates, requires fictitious forces to describe Newton's laws.
Real-world uses
- Engineers analyse passengers in an accelerating car from the car's frame.
- Weather models use rotating frames to include Earth's rotation.
- A passenger in a braking car is thrown forward, which is explained by working in the car frame with a fictitious force.
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Frequently asked questions
Is the Earth an inertial frame?
Approximately, for many experiments, but it rotates and accelerates slightly, so the approximation has limits.
How can I tell if a frame is inertial?
If a free object moves in a straight line at constant speed, the frame is inertial.
How do I tell if a frame is inertial?
A frame is inertial if objects with no net force move at constant velocity in it. A frame that accelerates or rotates is not inertial.
Related topics in Kinematics
Motion in three dimensions · Parametric motion · Galilean transformation · Coriolis and fictitious motion · Chase and meeting problems · Average vs instantaneous acceleration