# Angular acceleration of a softball

• physics1234
In summary, the "windmill" delivery method for pitching a softball involves rotating the arm 360° in a vertical plane before releasing the ball at the lowest point of the motion. An experienced pitcher can throw the ball with a speed of 89.0 mi/h, assuming uniform angular acceleration throughout the pitching motion. To find the angular acceleration, you will need to use the equations of angular motion kinematics, which are similar to linear kinematics equations.
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?

physics1234 said:
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

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.

## What is angular acceleration?

Angular acceleration is the rate of change of angular velocity over time. It is a measure of how quickly the rotational speed of an object is changing.

## How is angular acceleration different from linear acceleration?

Angular acceleration is a measure of how quickly an object's rotational speed changes, while linear acceleration is a measure of how quickly an object's linear speed changes. In other words, angular acceleration involves changes in direction, while linear acceleration involves changes in speed.

## How is angular acceleration related to the angular velocity of a softball?

Angular acceleration and angular velocity are directly related. Angular acceleration is equal to the change in angular velocity divided by the change in time. This means that the faster the softball's angular velocity changes, the higher its angular acceleration will be.

## What factors can affect the angular acceleration of a softball?

The angular acceleration of a softball can be affected by several factors, including the force applied to the softball, the mass and shape of the softball, and the distance between the axis of rotation and the point where the force is applied.

## How can angular acceleration be calculated for a softball?

The formula for calculating angular acceleration is: angular acceleration = (final angular velocity - initial angular velocity) / time. This means that to calculate angular acceleration for a softball, you need to know its final and initial angular velocities, as well as the time over which the change in velocity occurred.

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