If theta(t) is the angle between the path of a moving object and a fixed ray (se
ID: 2832253 • Letter: I
Question
If theta(t) is the angle between the path of a moving object and a fixed ray (see the figure below), the angular velocity of the object is omega(t)=theta'(t) and the angular acceleration of the object is alpha(t)=omega'(t).
Suppose a baseball batter rotates a bat through an angle of pi/2 with a constant angular acceleration of alpha rad/s2. If the tip of the bat is located 2.2 feet from the pivot point (the batter's body), the (linear) speed of the tip of the bat is v=2.2(omega). Find the value of alpha that will produce a speed of 129 mph for the tip of the bat at impact. Round to the nearest integer.
PLEASE SHOW WORK. Thanks!
Explanation / Answer
v = 120 mph = 176 fps
v = 2.2 (omega) = 176
=> omega = 80 rad/s
theta = pi/2
alpha = (omega)^2 / 2*Theta
=> alpha = 2038 rad/s^2