Obtaining velocity or acceleration vector of a point on a rigid body?

Question

If I have a cube that is moving at a velocity of $v$ and spinning at an angular velocity of $\omega$, how can I determine the instantaneous velocity vector of one of the vertices of the cube?

What if the cube is accelerating? And what if it had angular acceleration, $\alpha$? Would this change the method of calculation?

Would it be possible to get an acceleration vector?

score 3 · Accepted Answer · answered Aug 08 '13 at 15:04

3

The total velocity will be the sum of the translational and rotational velocities. Thus $$ \mathbf{v}_\text{net}=\mathbf{v}_\text{COM}+\mathbf{\omega}\times \mathbf r, $$ where $\mathbf r$ is the vector from the center of mass to the vertex, and $\mathbf v_\text{COM}$ is the center of mass velocity.

answered Aug 08 '13 at 15:04

Emilio Pisanty

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Note that $\times$ is the cross product operator. – John Alexiou Aug 08 '13 at 16:43
+1. $r$ is the vector distance from the CM to the vertex? – Daniel Aug 08 '13 at 17:13
Would there be any difference if the cube was accelerating? – Daniel Aug 08 '13 at 17:14
And would it be possible to get linear acceleration vector? – Daniel Aug 08 '13 at 17:26
I should refer you to any classical mechanics textbook, where all this is treated. For accelerations you can try this question. – Emilio Pisanty Aug 08 '13 at 19:28

Obtaining velocity or acceleration vector of a point on a rigid body?

1 Answers1