A CIRCULAR SAW BLADE ROTATING AT 15 REV/S IS BROUGHT TO A STOP IN 125 REV.
WHAT IS THE VALUE OF WO IN RAD/S?
94.2 RAD/S
WHAT IS THE SIZE OF THE DISPLACEMENT, TEITA, IN RADIANS?
WHAT IS THE SIZE OF THE ANGULAR ACCELERATION EXPERIENCED?
HOW LONG DID IT TAKE FOR THE SAW BLADE TO COME TO REST?
15*2 pi = 30 pi = 94.2 sure enough
average w during stop = wo/2 = 47.1 or 7.5 rev/s
time to stop = 125/7.5 = 16.7 seconds
w = wo + a t
0 = 94.2 + a (16.7)
so
a = -5.65 rad/s^2
so
theta = wo t + (1/2) a t^2
= 94.2 (16.7) - 2.83 * 16.7^2
1573 - 789
= 784 radians
To find the displacement, angular acceleration, and duration, we need more information. Specifically, we need the initial angular velocity (ωi) and the angular deceleration (α).
To calculate the size of the displacement, teita, in radians, we need to understand that the displacement is the difference in the initial and final angles of rotation.
Given that the circular saw blade is rotating at 15 rev/s and comes to a stop in 125 rev, we can determine the initial and final angles of rotation.
The initial angle of rotation can be calculated by multiplying the initial rate of rotation (15 rev/s) by the time it takes for the saw blade to come to a stop.
Initial angle of rotation = (15 rev/s) x (time to stop)
Since we are given the final angle of rotation (125 rev) and we know the initial angle of rotation is 0 (since the blade starts from rest), the size of the displacement, teita, can be calculated as:
teita = Final angle of rotation - Initial angle of rotation
= 125 rev - 0 rev
= 125 rev
Now, to convert rev to radians, we need to multiply the displacement by 2π (since 1 revolution is equal to 2π radians):
teita = 125 rev x (2π radians/1 rev)
= 125 rev x 2π radians
= 250π radians
Therefore, the size of the displacement, teita, is 250π radians.
Next, to find the angular acceleration experienced, we need to use the formula:
Angular acceleration (alpha) = Change in angular velocity (delta_w) / Change in time (delta_t)
However, in this case, since the saw blade comes to a stop, the change in angular velocity (delta_w) is equal to the initial angular velocity (wo) because the final angular velocity is 0.
Thus, the angular acceleration (alpha) can be calculated as:
alpha = wo / delta_t
Using the given data, wo (initial angular velocity) is 15 rev/s, and the saw blade takes time to stop. Unfortunately, the time it takes for the saw blade to come to rest is not provided, so the calculation cannot be completed without this information.
Therefore, we cannot determine the size of the angular acceleration or the time it took for the saw blade to come to rest without knowing the time it takes for the saw blade to come to rest.