Anglar motion, where do i start

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In summary, to calculate the final position and x,y velocities of a point on a Cartesian plane after rotating around another point, use complex algebra. Express the position and velocity in terms of x + iy and Vx + iVy respectively, then multiply by cos(ang) + i sin(ang) where ang is the angle of rotation. Transform the resulting values back to the original origin.
  • #1
jsm6252
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Homework Statement


How do i work out the final position and x,y velocities of a single point on a cartesian plane after it rotates around another point. We are given an initial x,y velocity.


Homework Equations


unknown at this stage


The Attempt at a Solution

 
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  • #2
The easiest way (in my opinion) is with complex algebra. Find the position of your single point with respect to the rotation center and express it as x + iy. Express the velocity as Vx + iVy. Multiply each by cos(ang) + i sin(ang) where ang is the angle of rotation. Transform the resulting x & y values back to the original origin. (The rotated velocity is ok as it is.)
 
  • #3
thank you
i'll try and do some research
 

1. What is angular motion?

Angular motion refers to the movement of an object along a circular path or rotation around a central point. It involves both linear and rotational motion and is commonly seen in objects such as wheels, gears, and planets.

2. How is angular motion different from linear motion?

Linear motion involves movement along a straight line, while angular motion involves movement along a circular path or rotation around a central point. Linear motion can be described by displacement, velocity, and acceleration, while angular motion is described by angular displacement, angular velocity, and angular acceleration.

3. What are some examples of angular motion in everyday life?

Some examples of angular motion in everyday life include the rotation of the Earth around the sun, the spinning of a bicycle wheel, and the rotation of a ceiling fan. Other examples include the motion of a record player, the swing of a pendulum, and the turning of a car's steering wheel.

4. What factors affect angular motion?

The factors that affect angular motion include the mass of the object, the distance from the central point, the angular velocity, and the applied torque. Other factors such as friction and air resistance can also affect angular motion.

5. How do I calculate angular motion?

To calculate angular motion, you will need to use equations such as angular displacement = angular velocity x time, angular velocity = angular acceleration x time, and torque = moment of inertia x angular acceleration. These equations can be derived from Newton's laws of motion and are used to describe the relationship between the different variables in angular motion.

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