Question

At its peak, a tornado is 50 m in diameter and carries 675 km/h winds. What is its angular velocity in revolutions per second? unit = لها

Answer 1

1.19 revolutions per second

Answer 2

The angular velocity of a tornado can be calculated by first finding the linear velocity at its edge and then converting it to angular velocity. To find the linear velocity, we need to convert the diameter from meters to kilometers and the unit of time from hours to seconds.

Given that the diameter of the tornado is 50 m and its wind speed is 675 km/h, we can find the linear velocity using the formula:

`\displaystyle \text{Linear velocity} = \text{wind speed} * \frac{\text{diameter}}{2}`

Converting the diameter to kilometers:

`\displaystyle \text{Diameter} = 50 \, \text{m} = 50 * 10^(-3) \, \text{km}`

Now we can calculate the linear velocity:

`\displaystyle \text{Linear velocity} = 675 \, \text{km/h} * \frac{50 * 10^(-3) \, \text{km}}{2}`

Simplifying the equation:

`\displaystyle \text{Linear velocity} = 675 * (50 * 10^(-3))/(2) \, \text{km/h}`

`\displaystyle \text{Linear velocity} = 16.875 \, \text{km/h}`

To convert the linear velocity to angular velocity, we need to convert kilometers per hour to kilometers per second. There are 3600 seconds in an hour, so:

`\displaystyle \text{Angular velocity} = \frac{\text{Linear velocity}}{\text{Diameter}} * \frac{1 \, \text{revolution}}{2 \pi \, \text{km}}`

Converting the linear velocity to kilometers per second:

`\displaystyle \text{Linear velocity} = 16.875 \, \text{km/h} = (16.875)/(3600) \, \text{km/s}`

Now we can calculate the angular velocity:

`\displaystyle \text{Angular velocity} = ((16.875)/(3600))/(50 * 10^(-3)) * \frac{1 \, \text{revolution}}{2 \pi \, \text{km}}`

Simplifying the equation:

`\displaystyle \text{Angular velocity} = (16.875)/(3600) * (1)/(50 * 10^(-3) * 2 \pi) \, \text{revolutions/s}`

Calculating the numerical value:

`\displaystyle \text{Angular velocity} \approx 7.14 * 10^(-5) \, \text{revolutions/s}`

Therefore, the angular velocity of the tornado is approximately
`\displaystyle 7.14 * 10^(-5)` revolutions per second. The unit for angular velocity is independent of language, so it remains as revolutions per second.

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