Rotating initially at 1800 rpm, a wheel with a diameter of 74.0 cm is brought to rest in 11.0 s. Calculate the magnitude of its angular acceleration in radians/second^2
The wheel radius makes no difference. They want an ANGULAR acceleration (or, in this case, deceleration) rate.
So, convert 1800 rpm to radians/s (which you surely know how to do) and divide the result by 11.0 seconds.
You should strictly put a minus sign in front of the number, to indicate deceleration.
so do you not need the diameter for anything?
If you don't need the radius, you don't need the diameter
To calculate the magnitude of the wheel's angular acceleration in radians per second squared, we need to use the following formula:
Angular acceleration = (Final angular velocity - Initial angular velocity) / Time
First, let's convert the initial angular velocity from rpm (revolutions per minute) to radians per second:
Initial angular velocity = 1800 rpm
1 revolution = 2π radians
1 minute = 60 seconds
So, the initial angular velocity in radians per second is:
Initial angular velocity = (1800 rpm) * (2π radians / 1 revolution) * (1 revolution / 60 seconds)
Initial angular velocity = (1800 * 2π) / 60 radians/second
Next, let's calculate the final angular velocity:
The wheel is brought to rest, so the final angular velocity is 0 radians per second.
Now, we can substitute the values into the formula:
Angular acceleration = (Final angular velocity - Initial angular velocity) / Time
Angular acceleration = (0 - [(1800 * 2π) / 60]) / 11
Finally, let's simplify the expression:
Angular acceleration = (-[(1800 * 2π) / 60]) / 11
Angular acceleration = -[(1800 * 2π) / (60 * 11)]
Angular acceleration ≈ -17.96 radians/second^2
Therefore, the magnitude of the wheel's angular acceleration is approximately 17.96 radians per second squared.