Game Development Reference
In-Depth Information
Figure 2-9. Circular path of particles making up a rigid body
The formula relating arc length to angular displacement is:
c = r Ω
where Ω must be in radians, not degrees. If you differentiate this formula with respect
to time:
dc/dt = r dΩ/dt
you get an equation relating the linear velocity of the particle as it moves along its circular
path to the angular velocity of the rigid body. This equation is written as follows:
v = r ω
This velocity as a vector is tangent to the circular path swept by the particle. Imagine
this particle as a ball at the end of a rod where the other end of the rod is fixed to a
rotating axis. If the ball is released from the end of the rod as it rotates, the ball will fly
off in a direction tangent to the circular path it was taking when attached to the rod.
This is in the same direction as the tangential linear velocity given by the preceding
equation. Figure 2-10 illustrates the tangential velocity.
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