Angular acceleration of a softball

[physics1234]

One method of pitching a softball is called the "windmill" delivery method, in which the pitcher's arm rotates through approximately 360° in a vertical plane before the 198 gram ball is released at the lowest point of the circular motion. An experienced pitcher can throw a ball with a speed of 89.0 mi/h. Assume that the angular acceleration is uniform throughout the pitching motion, and take the distance between the softball and the shoulder joint to be 75.1 cm.

I found 89mph= 39.783m/s and the angular speed to be 8.4310rev/s. How do I find the angular acceleration from this?

 

[OlderDan]

One method of pitching a softball is called the "windmill" delivery method, in which the pitcher's arm rotates through approximately 360° in a vertical plane before the 198 gram ball is released at the lowest point of the circular motion. An experienced pitcher can throw a ball with a speed of 89.0 mi/h. Assume that the angular acceleration is uniform throughout the pitching motion, and take the distance between the softball and the shoulder joint to be 75.1 cm.

I found 89mph= 39.783m/s and the angular speed to be 8.4310rev/s. How do I find the angular acceleration from this?

You will want the angular speed to be in radians per second. You need to use the equations of angular motion kinematics. These are directly analogous to the more familiar equations of linear kinematics

http://online.cctt.org/physicslab/content/PhyAPC/lessonnotes/rotationalmotion/kinematics.asp

 

[kyle8921]

To find the angular acceleration, we can use the equation: ωf² = ωi² + 2αθ, where ωf is the final angular velocity, ωi is the initial angular velocity, α is the angular acceleration, and θ is the angle through which the arm rotates (360° or 2π radians in this case).

Since we know the initial angular velocity (ωi = 0), the final angular velocity (ωf = 8.4310 rev/s), and the angle of rotation (θ = 2π), we can rearrange the equation to solve for α:

α = (ωf² - ωi²)/2θ

Plugging in the values, we get:

α = (8.4310 rev/s)² / (2*2π rad)

= 35.55 rev/s²

To convert this to units of rad/s², we can use the conversion factor 1 rev/s² = 2π rad/s², giving us an angular acceleration of approximately 224.1 rad/s².

This means that the pitcher's arm is accelerating at a rate of 224.1 radians per second squared during the pitching motion. This information can be used to further analyze and improve the pitching technique, as well as to understand the forces and torques involved in the motion.