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I remembered a pretty high school problem from kinematics. But it seems it can help even undergraduates to develop their understanding of what a relative motion is.
Consider a railway circle of radius ##r##. Assume that a carriage running along this circle has a speed ##v##. See the picture. A fly ##M## flies in the opposite direction and has a speed ##u,\quad |OM|=b##. Find a speed of the fly relative to the carriage.
The obvious incorrect answer is ##u+v## while the correct answer is ##u+bv/r##.
The point is as follows. The velocity of any point is defined relative to a frame. To say "velocity relative to the carriage" is the same as to say "velocity relative to a frame connected with the carriage" Thus in this problem the frame rotates about the point ##O## with the angular velocity ##v/r##.
Consider a railway circle of radius ##r##. Assume that a carriage running along this circle has a speed ##v##. See the picture. A fly ##M## flies in the opposite direction and has a speed ##u,\quad |OM|=b##. Find a speed of the fly relative to the carriage.
The obvious incorrect answer is ##u+v## while the correct answer is ##u+bv/r##.
The point is as follows. The velocity of any point is defined relative to a frame. To say "velocity relative to the carriage" is the same as to say "velocity relative to a frame connected with the carriage" Thus in this problem the frame rotates about the point ##O## with the angular velocity ##v/r##.
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