Linear Velocity

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If the position of an object to a Reference Frame varies with time.

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Example - Velocity of fixed point on rotating disk

Goal: Find ${\vec{v}}_{B/0}$

How: We know that $r_{B/0}=R{\vec{k}}_b$ and ${\vec{\omega }}_{b/0}=\dot{\theta }{\vec{i}}_b$. Then we get.

$${\vec{v}}_{B/0}=\dot{\theta }{\vec{i}}_b\times R{\vec{k}}_b=-R\dot{\theta }{\vec{j}}_b$$

Alternatively you can also do this without the b-frame, and achieve the same result (see the lecture notes).