CODEWITHSUNDEEP
c#c#-4.0physicsxna-4.0game-physics
ares_games
ares_games

Reputation: 1067

Implementation of velocity transformation during release of an object from a swinging rope

I have the following problem in two dimensions:

An object is attached to a rope and moving like a pendulum with the angular velocity V_a (polar angle per second), the rope has a length of L from the attachment point to the object. Now the rope is cut and the velocity of the object that was attached to the rope a moment ago should be smoothly transformed into V_xy, a two-dimensional velocity vector tangential to the circular movement on the rope.

The direction of V_xy is obtained by adding (or substracting, depending on the direction of movement) Pi/2 to the angle between the point of attachment and the object.

However, how can one obtain the absolute value (components) of the vector V_xy such that it corresponds to V_a ?

Lateron, it should be implemented in C#4 and XNA as part of a game.

Upvotes: 1

Views: 306

Answers (1)

MoonKnight
MoonKnight

Reputation: 23831

At the point the pendulum bob gets released (i.e. the rope snaps/is cut) you know the angle that the string makes with the vertical (call it angle A). From this the two values of the velocity are given by:

v_x = U * cos(A)

and

v_y = U * sin(A)

where U is the velocity of the bob in the direction of rotation (i.e. perpendicular to the string) at the time of release. If you have the angular velocity V_a and the string length L, then U can be established via:

U = V_a * L

and the equations above become

v_x = V_a * L * cos(A)

and

v_y = V_a * L * sin(A)

I hope this helps.

Upvotes: 1

Related Questions