An object is spinning at 4 rev/s and starts deccelarting at .9 rev/s^2. How long will it take the object to stop?
a = -.9(2pi) rad/s^2
then
v = -.9(2pi)t + c
when t=0, v=4(2pi)
so c= 8pi
then v = (-1.8pi)t + 8pi
we want v = 0
0 = (-1.8pi)t + 8pi
t = 40/9 seconds
or
just thinking about it, it loses .9revs per second, so 4/.9 = 40/9
(sometimes thinking within the box gets you trapped in the box)
Why did the object go to the gym?
Because it wanted to work on its spin cycle!
But seriously, let's calculate how long it will take for the object to stop. We can use the formula for deceleration:
ωf = ωi + αt
Where ωf is the final angular velocity, ωi is the initial angular velocity, α is the angular acceleration (or deceleration), and t is the time.
Since the object is spinning at 4 rev/s initially and decelerating at 0.9 rev/s^2, we can plug in these values:
0 = 4 rev/s + (-0.9 rev/s^2)t
Simplifying this equation, we get:
-4 rev/s = -0.9 rev/s^2 * t
Dividing both sides by -0.9 rev/s^2, we find:
t = 4 rev/s / 0.9 rev/s^2
Calculating this, we find:
t ≈ 4.44 s
So, it will take approximately 4.44 seconds for the object to stop spinning. Just enough time for a spin cycle!
To determine how long it will take for the object to stop spinning, we can use the formula:
ω = ω0 + αt
Where:
ω = final angular velocity (in rev/s)
ω0 = initial angular velocity (in rev/s)
α = angular acceleration (in rev/s^2)
t = time (in seconds)
Given:
ω0 = 4 rev/s
α = -0.9 rev/s^2 (negative sign indicates deceleration)
We want to find the time it takes for ω = 0. So we can rewrite the formula as:
0 = ω0 + αt
Substituting the known values:
0 = 4 rev/s + (-0.9 rev/s^2) * t
Now, let's solve for t:
-4 rev/s = -0.9 rev/s^2 * t
Divide both sides by -0.9 rev/s^2:
-4 rev/s / -0.9 rev/s^2 = t
t ≈ 4.44 s
Therefore, it will take approximately 4.44 seconds for the object to stop spinning.
To find out how long it will take for the object to stop spinning, we can use the formula for angular acceleration:
angular acceleration (α) = change in angular velocity (ω) / time (t)
In this case, the initial angular velocity (ω_i) is given as 4 rev/s, the final angular velocity (ω_f) is 0 rev/s (as the object stops spinning), and the angular acceleration (α) is -0.9 rev/s^2 (negative because it is decelerating).
Using the formula, we can rearrange it to solve for time (t):
α = (ω_f - ω_i) / t
Rearranging the formula:
t = (ω_f - ω_i) / α
Plugging in the values we have:
t = (0 rev/s - 4 rev/s) / -0.9 rev/s^2
Simplifying the expression:
t = 4 rev/s / 0.9 rev/s^2
Now, we can calculate the time it will take for the object to stop:
t = 4.44 s
Therefore, it will take approximately 4.44 seconds for the object to stop spinning.