The initial angular velocity and the angular acceleration of four rotating objects at the same time instant in time are listed in the table that follows. For each of the object determine the final angular speed after an elapsed time of 2s (c) initial angular velocity Wo -13.0 rad/s angular acceleration a +5.0 rad/s^2
To determine the final angular speed of each object after an elapsed time of 2s, we can use the following formula:
ωf = ωi + αt
where:
ωf = final angular speed
ωi = initial angular velocity
α = angular acceleration
t = elapsed time
For each object:
1) Object 1:
ωi = -13.0 rad/s
α = 5.0 rad/s^2
t = 2s
ωf = -13.0 rad/s + (5.0 rad/s^2)(2s) = -13.0 rad/s + 10.0 rad/s = -3.0 rad/s
Therefore, the final angular speed of object 1 after 2s is -3.0 rad/s.
2) Object 2:
ωi = -13.0 rad/s
α = 5.0 rad/s^2
t = 2s
ωf = -13.0 rad/s + (5.0 rad/s^2)(2s) = -13.0 rad/s + 10.0 rad/s = -3.0 rad/s
Therefore, the final angular speed of object 2 after 2s is -3.0 rad/s.
3) Object 3:
ωi = -13.0 rad/s
α = 5.0 rad/s^2
t = 2s
ωf = -13.0 rad/s + (5.0 rad/s^2)(2s) = -13.0 rad/s + 10.0 rad/s = -3.0 rad/s
Therefore, the final angular speed of object 3 after 2s is -3.0 rad/s.
4) Object 4:
ωi = -13.0 rad/s
α = 5.0 rad/s^2
t = 2s
ωf = -13.0 rad/s + (5.0 rad/s^2)(2s) = -13.0 rad/s + 10.0 rad/s = -3.0 rad/s
Therefore, the final angular speed of object 4 after 2s is -3.0 rad/s.