The angular speed of an engine wheel making `90" rev"//"min"` is

Options

A. `1.5 pi" rad"//s`
B. `3pi" rad"//s`
C. `4.5 pi" rad"//s`
D. `6 pi" rad"//s`

Answer

To find the angular speed of an engine wheel making 90 revolutions per minute, we can follow these steps:

### Step 1: Understand the relationship between revolutions per minute and angular speed
The angular speed (ω) in radians per second can be calculated using the formula:
\[ \omega = \frac{2 \pi n}{60} \]
where \( n \) is the number of revolutions per minute (rpm).

### Step 2: Substitute the given value into the formula
In this case, the engine wheel makes \( n = 90 \) revolutions per minute. We substitute this value into the formula:
\[ \omega = \frac{2 \pi \times 90}{60} \]

### Step 3: Simplify the expression
Now, we can simplify the expression:
\[ \omega = \frac{2 \pi \times 90}{60} = \frac{180 \pi}{60} \]
Next, we can simplify \( \frac{180}{60} \):
\[ \frac{180}{60} = 3 \]
Thus, we have:
\[ \omega = 3 \pi \text{ radians per second} \]

### Step 4: State the final answer
The angular speed of the engine wheel is:
\[ \omega = 3 \pi \text{ radians per second} \]

### Final Answer
The angular speed of the engine wheel is \( 3 \pi \) radians per second.

---