The rotational velocity of a merry-go-round increases at a constant rate from 1 rad/s to 2.1 rad/s in a time of 5.8 s. What is the rotational acceleration of the merry-go-round?
a=�� change in w divided by change in t
(Wfinal- Winitial)/ time
(2.1-1)/5.8
=0.189655172 rad/s ^2
Well, well, well, looks like the merry-go-round is getting ready to join the gym! Let's calculate its rotational acceleration, shall we?
The change in rotational velocity (Δω) is equal to the final rotational velocity (ωf) minus the initial rotational velocity (ωi). So, Δω = ωf - ωi = 2.1 rad/s - 1 rad/s = 1.1 rad/s.
Now, we know that the time it takes for this change to occur is 5.8 seconds. So, the rotational acceleration (α) can be calculated using the formula:
α = Δω / t,
where α is the rotational acceleration, Δω is the change in rotational velocity, and t is the time taken. Plugging in the given values, we have:
α = 1.1 rad/s / 5.8 s,
Calculating that, we find that the rotational acceleration of the merry-go-round is approximately:
α ≈ 0.1896 rad/s^2.
So, it seems like our merry-go-round is working hard to spin faster. But don't worry, I hear it enjoys being dizzy!
To find the rotational acceleration of the merry-go-round, we can use the formula:
Rotational acceleration = (Rotational final velocity - Rotational initial velocity) / Time
Given:
Rotational initial velocity (ω₁) = 1 rad/s
Rotational final velocity (ω₂) = 2.1 rad/s
Time (t) = 5.8 s
Plugging the values into the formula, we get:
Rotational acceleration = (2.1 rad/s - 1 rad/s) / 5.8 s
Calculating the numerator first:
Rotational acceleration = 1.1 rad/s / 5.8 s
Finally, evaluating the division:
Rotational acceleration ≈ 0.19 rad/s²
Therefore, the rotational acceleration of the merry-go-round is approximately 0.19 rad/s².
To find the rotational acceleration of the merry-go-round, we can use the formula for rotational acceleration:
Rotational acceleration = (Final rotational velocity - Initial rotational velocity) / Time
Given:
Initial rotational velocity (ω₁) = 1 rad/s
Final rotational velocity (ω₂) = 2.1 rad/s
Time (t) = 5.8 s
Substituting these values into the formula, we get:
Rotational acceleration = (2.1 rad/s - 1 rad/s) / 5.8 s
Simplifying, we have:
Rotational acceleration = 1.1 rad/s / 5.8 s
Now, let's divide the numerator by the denominator:
Rotational acceleration ≈ 0.1897 rad/s²
Therefore, the rotational acceleration of the merry-go-round is approximately 0.1897 rad/s².