The initial angular velocity and angular acceleration of four rotating objects at the same instant in time are listed in the table that follows. For each of the objects determine the final angular speed after an elapsed time 2s (a) initial angular velocity +13.0 rad/s Wo, angular 5.0 rad/s^2 acceleration a

Question

The initial angular velocity and angular acceleration of four rotating objects at the same instant in time are listed in the table that follows. For each of the objects determine the final angular speed after an elapsed time 2s (a) initial angular velocity +13.0 rad/s Wo, angular 5.0 rad/s^2 acceleration a

Answer 1

To find the final angular speed after 2s, we can use the following equation:

Final angular speed (ωf) = Initial angular velocity (ωo) + (Angular acceleration (α) × time (t))

Using the values given in the table:

Object 1:
Initial angular velocity (ωo) = +13.0 rad/s
Angular acceleration (α) = 5.0 rad/s^2
Time (t) = 2s

Substituting the values into the equation:
ωf = 13.0 rad/s + (5.0 rad/s^2 × 2s)
ωf = 13.0 rad/s + 10.0 rad/s
ωf = 23.0 rad/s

Therefore, the final angular speed for Object 1 after 2s is 23.0 rad/s.

Similarly, you can use the above equation to find the final angular speed for Objects 2, 3, and 4 using their respective initial angular velocities (ωo) and angular accelerations (α), along with a time of 2s.