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Vector uses in physics – Calculate velocity and acceleration – Exercise 3844

Exercise

A particle moves according to the law of motion

$$\vec{r}(t)=\cos(\alpha)\cos(\omega t)\vec{i}+\sin(\alpha)\cos(\omega t)\vec{j}+\sin(\omega t)\vec{k}$$

Where

$$\omega>0$$

Calculate their velocity, acceleration and their values (vector sizes).

Final Answer

$$\vec{v}(t)=\omega\cos(\alpha)\sin(\omega t)\vec{i}-\omega\sin(\alpha)\sin(\omega t)\vec{j}+\omega\cos(\omega t)\vec{k}$$

$$|\vec{v}(t)|=\omega$$

$$\vec{a}(t)=-\omega^2\cos(\alpha)\cos(\omega t)\vec{i}-\omega^2\sin(\alpha)\cos(\omega t)\vec{j}-\omega^2\sin(\omega t)\vec{k}$$

$$|\vec{a}(t)|=\omega^2$$

Solution

Coming soon…

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