To find the angular velocity of the baseball bat when it strikes the ball, we can use the following kinematic equation for rotational motion:
ω = ω₀ + αt
where ω is the final angular velocity, ω₀ is the initial angular velocity, α is the angular acceleration, and t is the time.
In this case, we are given:
- Average angular acceleration (α) = 2.3 rad/s²
- Time (t) = 0.75 s
- Initial angular velocity (ω₀) is not specified, so we assume it starts from rest (ω₀ = 0).
Using the given values, we can calculate the final angular velocity (ω):
ω = ω₀ + αt ω = 0 + (2.3 rad/s²)(0.75 s) ω = 1.725 rad/s
Therefore, the angular velocity of the baseball bat when it strikes the ball at the end of a 0.75 s swing is approximately 1.725 rad/s.