A body performing uniform cicular motion completed 140 revolution in a second. Its angular speed is

Options

A. 880 rad/s
B. 440 rad/s
C. 220 rad/s
D. 240 rad/s

Answer

To find the angular speed of a body performing uniform circular motion that completes 140 revolutions in one second, we can follow these steps:

### Step 1: Understand the relationship between revolutions and radians
1 revolution is equal to \(2\pi\) radians. Therefore, to convert revolutions to radians, we multiply the number of revolutions by \(2\pi\).

### Step 2: Calculate the angular speed
Given that the body completes 140 revolutions in 1 second, we can calculate the angular speed (\(\omega\)) in radians per second using the formula:
\[ \omega = n \times 2\pi \]
where \(n\) is the number of revolutions per second.

### Step 3: Substitute the values
Substituting \(n = 140\):
\[ \omega = 140 \times 2\pi \]

### Step 4: Simplify the expression
Calculating \(140 \times 2\pi\):
\[ \omega = 280\pi \text{ radians per second} \]

### Step 5: Calculate the numerical value
Using the approximate value of \(\pi \approx 3.14\):
\[ \omega \approx 280 \times 3.14 = 879.2 \text{ radians per second} \]
Rounding this to the nearest whole number gives:
\[ \omega \approx 880 \text{ radians per second} \]

### Conclusion
Thus, the angular speed of the body is approximately \(880\) radians per second.

### Final Answer
The angular speed is \(880\) radians per second.

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