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course_planning:course_notes:relative_motion [2014/06/19 02:32] – [Relative velocity] caballero | course_planning:course_notes:relative_motion [2014/06/19 02:33] (current) – caballero | ||
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We need a way to describe measurements in frames that are moving relative to each other. Consider the example of the truck and the pitching machine in the video above. The truck moves to the left with a speed of 100km/hr while the baseball is fired from the truck to the right with a speed of 100km/hr. In the frame of the camera, which is on the ground, the baseball appears to have no horizontal velocity. ((When the baseball strikes the ground, it is spinning so it bounces off the ground and begins to move, but this not because it has any linear velocity in the fixed frame of the camera.)) | We need a way to describe measurements in frames that are moving relative to each other. Consider the example of the truck and the pitching machine in the video above. The truck moves to the left with a speed of 100km/hr while the baseball is fired from the truck to the right with a speed of 100km/hr. In the frame of the camera, which is on the ground, the baseball appears to have no horizontal velocity. ((When the baseball strikes the ground, it is spinning so it bounces off the ground and begins to move, but this not because it has any linear velocity in the fixed frame of the camera.)) | ||
- | ==== Relative velocity | + | ==== Computing relative velocities |
In the diagram below, the truck appears at the instant the baseball leaves the pitching machine. | In the diagram below, the truck appears at the instant the baseball leaves the pitching machine. | ||
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* →vB/G is the velocity of the baseball relative to the ground. | * →vB/G is the velocity of the baseball relative to the ground. | ||
- | They are related through vector addition: →vB/G=→vB/T+→vT/G= ⟨−100,0⟩ km/hr + ⟨100,0⟩ km/hr = ⟨0,0⟩ km/hr. This demonstrates that the velocity of the baseball with respect to the ground is zero. So, in general, the velocity of A with respect to C is the vector sum of the velocity of A with respect to B and the velocity of B with respect to C. Mathematically, | + | They are related through vector addition: →vB/G=→vB/T+→vT/G= ⟨−100,0⟩ km/hr + ⟨100,0⟩ km/hr = ⟨0,0⟩ km/hr. This demonstrates that the velocity of the baseball with respect to the ground is zero (as observed in the video). So, in general, the velocity of A with respect to C is the vector sum of the velocity of A with respect to B and the velocity of B with respect to C. Mathematically, |
→vA/C=→vA/B+→vB/C | →vA/C=→vA/B+→vB/C |