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Relative velocities between two particles in classical mechanics. The figure shows two objects A and B moving at constant velocity. The equations of motion are: = +, = +, where the subscript i refers to the initial displacement (at time t equal to zero).
Then, the velocity of object A relative to object B is defined as the difference of the two velocity vectors: = Similarly, the relative velocity of object B moving with velocity w, relative to object A moving with velocity v is: = Usually, the inertial frame chosen is that in which the latter of the two mentioned objects is in rest.
The proper length of an object is the length of the object in the frame in which the object is at rest. Also, this contraction only affects the dimensions of the object which are parallel to the relative velocity between the object and observer. Thus, lengths perpendicular to the direction of motion are unaffected by length contraction.
where r 0 and t 0 represent shifts in the origin of space and time, and v is the relative velocity of the two inertial reference frames. Under Galilean transformations, the time t 2 − t 1 between two events is the same for all reference frames and the distance between two simultaneous events (or, equivalently, the length of any object, | r 2 ...
The COR is a property of a pair of objects in a collision, not a single object. If a given object collides with two different objects, each collision has its own COR. When a single object is described as having a given coefficient of restitution, as if it were an intrinsic property without reference to a second object, some assumptions have been made – for example that the collision is with ...
During the collision of small objects, kinetic energy is first converted to potential energy associated with a repulsive or attractive force between the particles (when the particles move against this force, i.e. the angle between the force and the relative velocity is obtuse), then this potential energy is converted back to kinetic energy ...
The Milky Way Galaxy is moving through space and many astronomers believe the velocity of this motion to be approximately 600 kilometres per second (1,340,000 mph) relative to the observed locations of other nearby galaxies.
Time dilation is the difference in elapsed time as measured by two clocks, either because of a relative velocity between them (special relativity), or a difference in gravitational potential between their locations (general relativity). When unspecified, "time dilation" usually refers to the effect due to velocity.