When a perosn throws a meter stivk it is found that the centre of the stick is moving with speed `10 m//s` and left end stick with speed `20 m//s`. Both points move vertically upwards at that moment. Then angular speed the stick is :

Options

A. `20 rad//s`
B. `10 rad//s`
C. `30 rad//s`
D. None of these

Answer

To find the angular speed of the meter stick when it is thrown, we can follow these steps:

### Step 1: Understand the given information
- The center of the stick is moving with a speed of \( v_{cm} = 10 \, \text{m/s} \).
- The left end of the stick is moving with a speed of \( v_L = 20 \, \text{m/s} \).
- The length of the stick is \( L = 1 \, \text{m} \).

### Step 2: Determine the speed of the right end of the stick
Since the stick is uniform and the center of mass is at the midpoint, we can denote the speed of the right end as \( v_R \). The center of mass speed can be expressed as the average of the speeds of the two ends:

\[ v_{cm} = \frac{v_L + v_R}{2} \]

Substituting the known values:

\[ 10 = \frac{20 + v_R}{2} \]

### Step 3: Solve for \( v_R \)
Multiply both sides by 2 to eliminate the fraction:

\[ 20 = 20 + v_R \]

Now, isolate \( v_R \):

\[ v_R = 20 - 20 = 0 \, \text{m/s} \]

### Step 4: Calculate the angular speed
The angular speed \( \omega \) can be calculated using the formula:

\[ \omega = \frac{v_L - v_R}{R} \]

Where \( R \) is the distance from the center of mass to either end of the stick. Since the stick is 1 meter long, the distance from the center to either end is:

\[ R = \frac{L}{2} = \frac{1}{2} = 0.5 \, \text{m} \]

Substituting the values into the angular speed formula:

\[ \omega = \frac{20 - 0}{0.5} \]

### Step 5: Simplify the expression
\[ \omega = \frac{20}{0.5} = 40 \, \text{rad/s} \]

### Conclusion
The angular speed of the stick is \( 40 \, \text{rad/s} \).