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Is a rotating frame an inertial frame?
What is a rotating reference frame?
What is an inertial frame of reference?
How are the velocities in the inertial and rotating frame of reference related?
Why do laws of nature take a simpler form in inertial frames of reference?
How do you identify an inertial frame?
A rotating frame of reference is a special case of a non-inertial reference frame that is rotating relative to an inertial reference frame. An everyday example of a rotating reference frame is the surface of the Earth .
- Newton's 2nd Law
- Coordinate Representation, Change of Basis, Rotation Matrix
- Rotation Matrix
- Time Derivatives
The derivation of the Navier-Stokes equations is based on Newton's second law: It is assumed that the kinematics of a particle is determined by the particle's interaction with its physical environment. Every acceleration (change of velocity) is caused by an external force. If one eventually knows all relevant forces, the acceleration can be calcula...
Consider two cartesian coordinate system: One is inertial (inin) and the other one (rotrot) rotates with respect to the first one with constant angular velocity:Ω=dφdtΩ=dφdt(1)Without loss of generality, the zz-axes of both systems can be chosen to be aligned parallel to the axis of rotation. Then the relative orientation between the two coordinate...
The transformation matrix RR depends on the angle of rotation φ(t)φ(t) and contains the coordinates of the rotational unit vectors with respect to the inertial basis:R=([ˆxrot]in[ˆyrot]in[ˆzrot]in)=(cosφ−sinφ0sinφcosφ0001)R=([xrot]in[yrot]in[zrot]in)=⎛⎜⎝cosφ−sinφ0sinφcosφ0001⎞⎟⎠(5)(6)As it is characteristic for a rotation matrix,R−1=RTR−1=RT(7)sinc...
When the origins of the coordinates systems coincide, then the position vector →r→ris independent of the particular coordinate system, since it connects this common origin with a particle's location in space (which is also independent of the frame of reference).
Now let S be an inertial frame and S0 be a frame rotating with angular velocity ! with respect to S. Let {e 1,e 2,e 3} be a basis for S and {e0 1,e 0 2,e 0 3} a basis for S0. Let a be any vector — not necessarily fixed in either S or S 0— with components a i and a i respectively, i.e., a = a 1e 1 +a 2e 2 +a 3e 3 = a 0 1 e 0 1 +a 0 2 e 0 2 ...
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Dec 30, 2020 · Rotating reference frames are not inertial frames, as to keep something rotating (and thus change the direction of the linear velocity) requires the application of a net force.
In classical physics and special relativity, an inertial frame of reference (also called inertial space, or Galilean reference frame) is a stationary or uniformly moving frame of reference.
6.1 Rotating Frames. Let’s start with the inertial frame S drawn in the figure with coordinate axes x, y and z. Our goal is to understand. z=z. the motion of particles as seen in a non-inertial frame S0, with axes x0, y0 and z0, which is rotating with respect to S. We’ll denote the angle between the x-axis of S and the x0- y y. axis of S0 as .
Newton's second law, F = ma, is used to describe the motion of an object in response to an applied force, but that presumes that the observer is in a non-accelerating reference frame. The term "inertial frame" is commonly used to describe such a frame of reference.
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