Suppose a revolving door at the bank is spinning around once every 5 seconds. As you walk through, you push on the door for 2 seconds, which increases that rotational speed so that it rotates once a second. What was the Rotational acceleration due to your push?
To calculate the rotational acceleration, we need to use the equation:
Rotational acceleration (α) = Δω / Δt
Where:
- Δω represents the change in angular velocity (rotational speed)
- Δt represents the time interval over which the change occurs.
In this case, the initial rotational speed of the revolving door is one revolution every 5 seconds, or ω₁ = 1 revolution/5 seconds. After you push on the door for 2 seconds, the rotational speed increases to one revolution per second, or ω₂ = 1 revolution/1 second.
To find the change in angular velocity, we subtract the initial angular velocity from the final angular velocity:
Δω = ω₂ - ω₁
Substituting the values:
Δω = (1 revolution/1 second) - (1 revolution/5 seconds)
Δω = (5 revolutions/5 seconds) - (1 revolution/5 seconds)
Δω = (4 revolutions/5 seconds)
Next, we need to calculate the change in time:
Δt = 2 seconds
Now, we can substitute these values into the equation for rotational acceleration:
Rotational acceleration (α) = Δω / Δt
α = (4 revolutions/5 seconds) / (2 seconds)
Simplifying, we have:
α = 2 revolutions/5 seconds²
Therefore, the rotational acceleration due to your push on the revolving door is 2 revolutions per 5 seconds squared.