Question

When a person throws a meter stick it is found that the center of the stick is moving with a speed of 10 m/s vertically upwards & left end of the stick with a speed Of 20 m/s vertically upwards. Then the angular speed of the stick is:

Answer 1

Step 1: Given data

When a person throws a meter stick, the center of the stick moves vertically upwards at a speed of $10\mathrm{m}/\mathrm{s}$, and the left end moves vertically upwards at a speed of $20\mathrm{m}/\mathrm{s}$.

The speed of the center of the stick, $\mathrm{v}=10\mathrm{m}/\mathrm{s}$.

The speed of the left end of the stick,$V_P=20m/s$,

Let $r$ be the distance between the stick's endpoint and its center.

Here,

$\mathrm{r}=\frac{1}{2}\mathrm{m}$

Step 2: Formula used

${\mathrm{V}}_{\mathrm{p}}=\mathrm{v}+\mathrm{rw}$

Step 3: Calculation

By substituting the values in the above formula,

$$\begin{gathered} \Rightarrow 20=10+\frac{1}{2}\mathrm{w} \\ \mathrm{w}=20\mathrm{rad}/\mathrm{s} \end{gathered}$$

Therefore, the angular speed of the stick is $20\mathrm{rad}/\mathrm{s}$.