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

In summary, the conversation involves the topic of proving a simulation and determining the resulting ω and v of a cube with specific properties. The poster also asks for clarification on their calculations.
  • #1
calvinwylie
2
0
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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  • #2
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?
 
  • #3
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)
 

1. What is the difference between angular and linear velocity?

Angular velocity refers to the rate of change of angular displacement of a rigid body, while linear velocity refers to the rate of change of linear displacement. Simply put, angular velocity describes how fast an object is rotating, while linear velocity describes how fast an object is moving in a straight line.

2. How is angular velocity calculated?

Angular velocity is calculated by dividing the change in angular displacement by the change in time. It is typically measured in radians per second (rad/s).

3. Can a rigid body have different linear and angular velocities?

Yes, a rigid body can have different linear and angular velocities. This is because linear velocity depends on the speed and direction of the object's linear motion, while angular velocity depends on the speed and direction of the object's rotation.

4. How does a force affect the angular and linear velocity of a rigid body?

The force applied to a rigid body can change both its angular and linear velocity. The direction and magnitude of the force will determine how the velocities are affected. For example, a force applied perpendicularly to the axis of rotation will only change the angular velocity, while a force applied in the same direction as the linear motion will change both the angular and linear velocities.

5. Can the angular and linear velocity of a rigid body be constant?

Yes, it is possible for the angular and linear velocity of a rigid body to be constant. This would occur if the object is moving at a constant speed in a straight line or rotating at a constant speed without any external forces acting on it.

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