A wheel has an initial speed of 100 radians/s. It is then slowed down with a magnitude of the constant angular acceleration of 6.0s^-2. To make it come to rest, how many revolutions does it need to make?
(100/s)÷(6/s^2) = 100/6 s
It starts with a speed of 100, and loses 6 every second...
initial speed = 100
final speed = 0
so average speed = 50 rad/s
How long does it take?
v = Vi - 6 t
0= 100 - 6 t
t = 100/6 = 16.7 s
so radians total = 50*16.7
divide by 2pi rad/revolution
50 ( 16.7) /6.28 = answer
To find the number of revolutions the wheel needs to make to come to rest, we need to use the equations of rotational motion.
First, let's find the time it takes for the wheel to come to rest. We can use the equation:
ω_f = ω_i + α * t
Where:
ω_f is the final angular velocity (0 rad/s, as the wheel comes to rest)
ω_i is the initial angular velocity (100 rad/s)
α is the angular acceleration (-6.0 s^-2)
t is the time
Rearranging the equation, we can solve for t:
t = (ω_f - ω_i) / α
Since ω_f is 0 rad/s, the equation becomes:
t = -ω_i / α
Substituting the given values, we have:
t = -100 rad/s / (-6.0 s^-2) = 16.67 s
Next, let's find the total angular displacement of the wheel during this time. We can use the equation:
θ = ω_i * t + (1/2) * α * t^2
Since the wheel starts from rest at zero angular displacement, the equation simplifies to:
θ = (1/2) * α * t^2
Substituting the given values, we have:
θ = (1/2) * (-6.0 s^-2) * (16.67 s)^2 = 833.5 radians
To convert radians to revolutions, we use the conversion factor:
1 revolution = 2π radians
Therefore, the number of revolutions the wheel needs to make to come to rest is:
Number of revolutions = θ / (2π) = 833.5 radians / (2π) ≈ 132.58 revolutions
So, the wheel needs to make approximately 132.58 revolutions to come to rest.