Angular vleocity of a rotating object from 650degrees/s to 495degrees/s in 1.2 seconds. What is the angular acceleration
To find the angular acceleration, we can use the formula:
Angular acceleration (α) = (final angular velocity - initial angular velocity) / time
Given:
Initial angular velocity (ω1) = 650 degrees/s
Final angular velocity (ω2) = 495 degrees/s
Time (t) = 1.2 seconds
First, we need to convert the angular velocities from degrees/s to radians/s since the standard unit for angular velocity is radians.
To convert degrees to radians, we use the following conversion formula:
1 degree = π/180 radians
So, we have:
Initial angular velocity (ω1) = 650 degrees/s * π/180 radians/degree = 11.366 radians/s
Final angular velocity (ω2) = 495 degrees/s * π/180 radians/degree = 8.639 radians/s
Now, we can calculate the angular acceleration:
Angular acceleration (α) = (ω2 - ω1) / t
= (8.639 radians/s - 11.366 radians/s) / 1.2 s
= -2.727 radians/s²
Therefore, the angular acceleration of the rotating object is -2.727 radians/s². The negative sign indicates that the object is undergoing deceleration or slowing down.