First slide

Dynamics of uniform and non uniform circular motion

Question

A particle moves so that its position vector varies with time as $\vec{r} = A \cos ω t \hat{i} + A \sin ω t \hat{j}$ . The initial velocity of the particle is

Moderate

A

$A ω \hat{i}$
B

$A ω \hat{j}$
C

$A ω (\hat{i} + \hat{j})$
D

$A ω (\hat{i} - \hat{j})$

Solution

$Substituting \vec{r} = (A \cos ω t \hat{i} + A \sin ω t \hat{j}) in \vec{v} = \frac{d \vec{r}}{d t} we have$
$\begin{array}{l} \vec{v} = A \frac{d}{d t} (\cos ω t) \hat{i} + A \frac{d}{d t} (\sin ω t) \hat{j} \\ = - A ω \sin ω t \hat{i} + A ω \cos ω t \hat{j} \\ At t = 0, v = - A ω \sin 0 \hat{i} + A ω \cos 0 \hat{j} = A ω \hat{j} \end{array}$

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