Translation Translation involves the movement of a body along a straight line without changing the direction of its motion. For example, if a car moves forw...
Translation
Translation involves the movement of a body along a straight line without changing the direction of its motion. For example, if a car moves forward, its position will change along a horizontal line, but its direction of motion will remain the same.
Rotation
Rotation involves the movement of a body around a fixed point. For example, if a wheel is turned, it will rotate around its center point. The direction of rotation will also change, as the object will move around the fixed point.
The relationship between translation and rotation can be described by the following equations:
x' = x - vT
y' = y - vT
θ' = θ + ωT
where:
x', y', θ' are the coordinates of the body in the new frame of reference
x, y, θ are the coordinates of the body in the original frame of reference
v is the speed of the body
T is the time taken for the body to move from point A to point B
ω is the angular velocity of the body
These equations show that the position and velocity of a body in a new frame of reference can be found by subtracting the time taken for the body to move from point A to point B from the original coordinates and velocities. The angular velocity of a body can also be found by taking the derivative of the angle it rotates through in a given time interval