Exercise
A particle moves according to the law of motion
\vec{r}(t)=R\cos(\omega t)\vec{i}+R\sin(\omega t)\vec{j}
Where
\omega>0, R>0
Calculate the velocity function, the acceleration function, their values (vector sizes) and unit vectors.
Final Answer
\vec{v}(t)=-R\omega\sin(\omega t)\vec{i}+R\omega\cos(\omega t)\vec{j}
|\vec{v}(t)|=R\omega
\hat{v}(t)=-\sin(\omega t)\vec{i}+\cos(\omega t)\vec{j}
\vec{a}(t)=-R\omega^2\cos(\omega t)\vec{i}-R\omega^2\sin(\omega t)\vec{j}
|\vec{a}(t)|=R\omega^2
\hat{a}(t)=-\cos(\omega t)\vec{i}-\sin(\omega t)\vec{j}
Solution
Coming soon…
