A ceiling fan is rotating 245 times each minute. What is its frequency? What is its period of rotation? What is its angular velocity? When the fan is turned off, it slows down at 2.50 rad/s2 – how long will it take the fan to stop?

I will be happy to check your thinking on this.

f= 3.47/second

To determine the frequency of the ceiling fan, we can use the formula:

Frequency (f) = Number of rotations / Time

Given that the fan rotates 245 times each minute, we can convert this to seconds by dividing by 60:

Number of rotations / Time = 245 rotations / 60 seconds

Thus, the frequency of the ceiling fan is 4.083 Hz (Hertz).

To find the period of rotation, we can use the formula:

Period (T) = 1 / Frequency

Using the previously calculated frequency, we can determine the period:

Period (T) = 1 / 4.083 Hz

Therefore, the period of rotation for the ceiling fan is approximately 0.245 seconds (s).

Angular velocity (ω) is the rate at which an object rotates in radians per second. To find the angular velocity, we can use the formula:

Angular velocity (ω) = 2π * Frequency

Applying the given frequency of 4.083 Hz, we have:

Angular velocity (ω) = 2π * 4.083 Hz

Hence, the angular velocity of the ceiling fan is approximately 25.69 rad/s.

To determine how long it will take for the fan to stop when it is slowing down at a rate of 2.50 rad/s^2, we can use the formula:

Time (t) = Initial angular velocity (ω₀) / Angular deceleration (α)

The initial angular velocity (ω₀) can be obtained from the given angular velocity of the fan, which is 25.69 rad/s.

Using the formula, we have:

Time (t) = 25.69 rad/s / 2.50 rad/s^2

Hence, it will take approximately 10.28 seconds for the fan to stop.