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Straight-line motions[edit]

The principles described above are illustrated by considering two example motions: a straight-line motion as seen in a stationary frame, and a straight-line motion as seen in a rotating frame.

The first case, straight line motion as seen in a stationary frame, according to Newton's law of inertia, requires no force.^[1] However, in the rotating frame, this straight-line motion appears curved, and therefore the motion requires a force.^[2] How are these two pictures reconciled?

In the rotating frame there is always a centrifugal force, and if the object appears to move in the rotating frame in a direction at an angle to the axis of rotation, there also is a Coriolis force. In order for the rotating observer to agree with the stationary observer that the motion requires no external agency, the centrifugal force and the Coriolis force must combine in a manner that provides the force required by the curved motion, all by themselves.

In the second case, straight-line motion in as seen in a rotating frame, the roles of the observers are reversed. This time the rotating observer sees straight-line motion, and so finds no net force is needed to support the motion. On the other hand, the stationary observer sees a curved motion, and so believes a external agency is required.^[3] How are these views reconciled?

Again, in the rotating frame there are always fictitious forces.^[4] If they are unopposed, they cause curved motion. Hence, the rotating observer seeing a straight-line motion must find an external agency at work that exactly balances these fictitious forces. Thus, the two observers again agree, this time that an external force is necessary.

References[edit]

^ Mitch Stokes (2010). Isaac Newton. Thomas Nelson Inc. p. 123. ISBN 1595553037. Unless a (net) force acts upon an object, it will either remain at rest or remain moving in a straight line at a constant speed.
^ Mitch Stokes (2010). Isaac Newton. Thomas Nelson Inc. p. 123. ISBN 1595553037. A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed.
^ Bruno Siciliano, Oussama Khatib (2008). Springer handbook of robotics. Springer. p. 481. ISBN 354023957X. Suppose that an object moves along a straight line in a rotating frame of reference. To an outside observer in an inertial frame the object's path is curved – thus there must be some force acting on the object to maintain the straight line motion as viewed by the rotating observer.
^ Gregory K. McMillan, Douglas M. Considine (1999). Process/industrial instruments and controls handbook (5th ed.). McGraw-Hill Professional. p. 429. ISBN 0070125821. These forces are always present when translational (straight line) and rotational (revolving) movement occur simultaneously.

[Newton-1] Mitch Stokes (2010). Isaac Newton. Thomas Nelson Inc. p. 123. ISBN 1595553037. Unless a (net) force acts upon an object, it will either remain at rest or remain moving in a straight line at a constant speed.

[force-2] Mitch Stokes (2010). Isaac Newton. Thomas Nelson Inc. p. 123. ISBN 1595553037. A change in motion is proportional to the motive force impressed and takes place along the straight line in which that force is impressed.

[Khatib-3] Bruno Siciliano, Oussama Khatib (2008). Springer handbook of robotics. Springer. p. 481. ISBN 354023957X. Suppose that an object moves along a straight line in a rotating frame of reference. To an outside observer in an inertial frame the object's path is curved – thus there must be some force acting on the object to maintain the straight line motion as viewed by the rotating observer.

[McMillan-4] Gregory K. McMillan, Douglas M. Considine (1999). Process/industrial instruments and controls handbook (5th ed.). McGraw-Hill Professional. p. 429. ISBN 0070125821. These forces are always present when translational (straight line) and rotational (revolving) movement occur simultaneously.

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