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.

average speed= .35rev/s

so in 2.9 seconds, it goes...

b) well, when it is half done, 2.9/2 seconds has elapsed.

average speed= (.7+.35)/2
rev= avg speed*2.9/2 revs.

To answer these questions, we will use the formula for angular velocity:

ω = Δθ / Δt

where ω is the angular velocity in radians per second, Δθ is the change in angle in radians, and Δt is the change in time in seconds.

(a) To find the number of revolutions the fan makes in 2.9 seconds, we need to convert the time to radians. We know that 1 revolution is equal to 2π radians, so we can multiply the angular velocity by the time to get the change in angle:

Δθ = ω * Δt

Plugging in the values:

Δθ = 0.70 rev/s * 2.9 s = 2.03 rev

Therefore, the fan makes approximately 2.03 revolutions in 2.9 seconds.

(b) To find the number of revolutions the fan must make for its speed to decrease from 0.7 rev/s to 0.35 rev/s, we need to determine the change in angle. Since the fan is slowing down uniformly, the change in angular velocity is given by:

Δω = ω₂ - ω₁

where ω₁ is the initial angular velocity and ω₂ is the final angular velocity.

Plugging in the values:

Δω = 0.35 rev/s - 0.7 rev/s = -0.35 rev/s

Now, we can use the same formula as before to find the change in angle:

Δθ = Δω * Δt

Plugging in the values:

Δθ = -0.35 rev/s * Δt

To find the value of Δt, we can rearrange the formula and substitute ω = Δθ / Δt:

Δt = Δθ / Δω

Plugging in the values:

Δt = (-0.35 rev/s) / (-0.35 rev/s) = 1 s

Therefore, the fan must make approximately 1 revolution for its speed to decrease from 0.7 rev/s to 0.35 rev/s.