Final answer:
The average angular acceleration of the disk is approximately -182.76 rad/s². The magnitude of the tangential linear acceleration of a point 1/5 of the way out from the center of the disk is approximately 438.2 cm/s².
Step-by-step explanation:
To find the average angular acceleration of the disk, we need to determine the initial and final angular velocities of the disk, as well as the time taken for it to come to rest. The initial angular velocity is 4770 rpm, which is equivalent to 4770/60 = 79.5 rev/s. The final angular velocity is 0 rev/s. Converting the time to seconds gives us 0.435 s. The average angular acceleration is given by the formula:
angular acceleration = (final angular velocity - initial angular velocity) / time
Substituting the values into the formula:
angular acceleration = (0 - 79.5) / 0.435 = -182.76 rad/s² (rounded to two decimal places)
The magnitude of the average angular acceleration of the disk is thus approximately 182.76 rad/s².
To find the magnitude of the tangential linear acceleration of a point 1/5 of the way out from the center of the disk, we need to first find the angular acceleration using the formula:
angular acceleration = (linear acceleration) / (radius)
Since the radius of the disk is 12.0 cm and the point is 1/5 of the way out from the center, the radius at that point is 12.0 cm x (1/5) = 2.4 cm.
Substituting the values into the formula:
angular acceleration = (linear acceleration) / 2.4 cm
By rearranging the formula, we can find the linear acceleration:
linear acceleration = (angular acceleration) x (radius)
Substituting the values into the formula:
linear acceleration = (-182.76 rad/s²) x (2.4 cm) = -438.2 cm/s²
The magnitude of the tangential linear acceleration of the point is approximately 438.2 cm/s².