A ceiling fan is rotating at 0.70 rev/s. When turned off, it slows uniformly to a stop in 2.9 s.

(a) How many revolutions does it make in this time?
(b)Using the result from part (a), find the number of revolutions the fan must make for its speed to decrease from 0.7 rev/s to 0.35 rev/s.

Part A

using formula:

1/2(0+.7)*(174s)=60.9 for first answer
idk the background but thats is the answer......174 is from converting 2.9 to seconds
1 minute=60 seconds
2 minutes= another 60 seconds
.9 minutes=54 seconds
add the numbers up you get 174

for B i have no clue

To solve this problem, we'll use the equations of rotational motion.

(a) To find the number of revolutions the fan makes in 2.9 seconds, we need to calculate the initial angular velocity and the final angular velocity.

The initial angular velocity, ω_i, is given as 0.70 rev/s.

To find the final angular velocity, ω_f, we know that it slows uniformly to a stop. This means that the acceleration, α, is constant throughout the deceleration.

We can use the formula ω_f = ω_i + α * t, where t is the time and α is the angular acceleration.

Since it slows uniformly to a stop, the final angular velocity is 0 rev/s, and the time is 2.9 seconds.

Therefore, the angular acceleration, α, can be calculated as (ω_f - ω_i) / t.

Substituting the given values, we have α = (0 - 0.7 rev/s) / 2.9 s = -0.24 rev/s^2 (negative sign indicates deceleration).

Now, we can use the formula ω_f = ω_i + α * t to find the final angular velocity:

0 = 0.70 rev/s + (-0.24 rev/s^2) * 2.9 s.

Simplifying, we get 0 = 0.70 rev/s - 0.696 rev/s, which gives us ω_f = -0.696 rev/s.

But since we're interested in the number of revolutions, we'll take the absolute value:

|ω_f| = 0.696 rev/s.

Therefore, in 2.9 seconds, the fan makes approximately 0.696 revolutions.

(b) Now, let's calculate the number of revolutions the fan must make for its speed to decrease from 0.7 rev/s to 0.35 rev/s.

Using the initial angular velocity as 0.7 rev/s and the final angular velocity as 0.35 rev/s, we can calculate the deceleration by using the formula α = (ω_f - ω_i) / t.

Substituting the values, we have α = (0.35 rev/s - 0.7 rev/s) / t.

Since the deceleration is assumed to be constant, we can use the same value of -0.24 rev/s^2 calculated in part (a).

Rearranging the formula, we get t = (0.35 rev/s - 0.7 rev/s) / -0.24 rev/s^2.

Simplifying, we have t = -0.35 rev/s / -0.24 rev/s^2 = 1.46 s.

Therefore, the fan must make approximately 1.46 revolutions to decrease its speed from 0.7 rev/s to 0.35 rev/s.