Angular and linear velocity of a rigid body given a force.

AI Thread Summary
To determine the angular velocity (ω) and linear velocity (v) of a cube subjected to a force along the x-axis, the user references the equations ω = I⁻¹Lp and Lp = s x Mv, where I⁻¹ is the inverse of the inertia tensor, s is the position vector relative to the center of mass, M is the mass, and v is the velocity of the center of mass. The user is seeking validation of these equations in the context of their simulation, which involves a cube with specific dimensions and mass. A clarification is made regarding the position of the center of mass, as it is noted that (0,0,0.5) does not conform to the typical xy-plane definition. The discussion focuses on the correctness of the applied physics principles for simulating the cube's motion. Overall, the user is looking for confirmation of their approach to modeling the dynamics of a rigid body under force.
calvinwylie
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Hello,

I'm trying to prove a simulation of mine is working correctly. the simulation has a cube of sides 1, mass 1 and c.o.m. position at (0,0,0.5) ie sitting on the xy plane. i have a force along the x-axis of 10. Is there anyway given those two, that i can work out the resulting ω and v of the body? the cube is unconstrained.

this is my first post, so if I've done something wrong i apologise.

Thanks
 
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ok so i think I've found this:

ω = I-1Lp

where I-1 is the inverse of the inertia tensor. Lp is the angular momentum of the point the force is exerted on.

Lp = s x Mv.

where s is the position vector of the point relative to the center of mass. M is mass of the object and v is the velocity of the com.

Can someone at least tell me if this is correct?
 
calvinwylie said:
Hello,

I'm trying to prove a simulation of mine is working correctly. the simulation has a cube of sides 1, mass 1 and c.o.m. position at (0,0,0.5) ie sitting on the xy plane. i have a force along the x-axis of 10.
Thanks

How is (0,0,0.5) on the xy plane? One ussually takes the order (x,y,z)
 

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