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How to Calculate the 3D Rotational Motion

Rotational motion can be calculated for any object if you have certain data. You must have the starting position of the object along the x, y and z axes, the speed at which the object rotates, and the change in speed or acceleration. The rotational motion is calculated for each axis independently, giving you three points in space after a certain time has elapsed. This calculation is very useful for solving certain types of physics problems.

Things You'll Need

Calculator

Instructions

- 1
  Calculate the position of the rotating point in the x-axis, given the original position (X0), the velocity (Vx) and the acceleration (Ax). The position of the object after time (T) is expressed using the following equation (T^2 means T to the power of 2):
  
  X = X0 + Vx * T + (0.5) * Ax * T^2
- 2
  Calculate the position of the rotating point in the y-axis, given the original position (Y0), the velocity (Vy) and the acceleration (Ay). The position of the object after time is expressed using the following equation:
  
  Y = Y0 + Vy * T + (0.5) * Ay * T^2
- 3
  Calculate the position of the rotating point in the z-axis, given the original position (Z0), the velocity (Vz) and the acceleration (Az). The position of the object after time is expressed using the following equation:
  
  Z = Z0 + Vz * T + (0.5) * Az * T^2
- 4
  Solve the three equations given the following initial conditions: X0 = 0; Y0 = 0; Z0 = 0; Vx = 1: Vy = 2; Vz = 3; Ax = 0; Ay = 1; Az = 2; and T = 1. When you substitute these numbers into the three equations, you end up with the following expressions:
  
  X = 0 + (1 * 1) + (0 * 1^2) = 1
  Y = 0 + (2 * 1) + (1 * 1^2) = 3
  Z = 0 + (3 * 1) + (2 * 1^2) = 5

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