Homework help for mastering physics

In summary, a baseball player catches a line drive while leaping vertically into the air. The ball has a mass of 145 and is headed horizontally towards the player's glove. After catching the ball, the player's angular speed around a vertical axis through his head and feet is being calculated assuming he was stationary at the time of the catch. To make the calculation reasonable, the player's body is modeled as a uniform solid cylinder with a mass of 73.0 and diameter of 35.0, and his arms are modeled as thin rods, each 70.0 long, pivoting around a vertical axis through his center. This problem likely involves conservation of angular momentum, specifically in an inelastic collision.
  • #1
jesi007
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An 85.0 baseball player who has leapt vertically into the air to catch a line drive catches the ball as it is headed horizontally directly into his glove. The ball has a mass of 145 and is headed perpendicular to his arm at 52.0 just before he catches it.

Just after he catches the ball with his arm extended horizontally, what is the player's angular speed about a vertical axis through his head and feet, assuming that he was stationary at the instant he caught it?

To make the calculations reasonable, you can model the player's body as a uniform solid cylinder of mass 73.0 and diameter 35.0 and his arms as thin 6.00 rods, each 70.0 long, pivoting around a vertical axis through his center.



Please help me with this homework problem someone! I believe this deals with conservation of angular momentum but please help me out on how to work this out. Thank you sooo much for you help!
 
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  • #3


I am happy to help you with this homework problem. First, let's break down the problem and identify the key concepts involved.

The problem involves a baseball player catching a ball while leaping vertically into the air. The ball has a certain mass and velocity, and the player's body and arms can be modeled as a uniform solid cylinder and thin rods, respectively. We are asked to calculate the player's angular speed about a vertical axis through his head and feet, assuming he was stationary at the instant he caught the ball.

To solve this problem, we need to apply the principle of conservation of angular momentum. This principle states that the total angular momentum of a system remains constant unless acted upon by an external torque. In this case, the system includes the player, the ball, and the axis of rotation.

We can calculate the initial angular momentum of the system before the player catches the ball by using the formula L = Iω, where L is angular momentum, I is moment of inertia, and ω is angular speed. The moment of inertia for a uniform solid cylinder is given by the formula I = ½MR^2, where M is mass and R is the radius of the cylinder. Using the given values, we can calculate the initial angular momentum of the system.

Next, we need to consider the change in angular momentum when the player catches the ball. Since the player's arms are initially extended horizontally, they will rotate about the vertical axis as he catches the ball. This change in angular momentum can be calculated by using the formula ΔL = IΔω, where ΔL is the change in angular momentum and Δω is the change in angular speed. The moment of inertia for thin rods rotating about their ends is given by the formula I = 1/3ML^2, where M is mass and L is the length of the rod. Using the given values, we can calculate the change in angular momentum.

Finally, we can use the principle of conservation of angular momentum to equate the initial and final angular momenta and solve for the final angular speed. Once we have the final angular speed, we can use it to calculate the player's angular speed about a vertical axis through his head and feet.

I hope this explanation helps you to understand the problem and how to solve it using the principle of conservation of angular momentum. Remember to always approach homework problems by breaking them down into smaller, manageable parts and applying the relevant concepts. Good
 

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