How Does Friction Affect the Angular Acceleration of a Sliding Bowling Ball?

AI Thread Summary
Friction significantly impacts the angular acceleration of a sliding bowling ball by affecting its translational deceleration. The initial deceleration of the ball is 5.886 m/s², but using the formula α = a/R led to confusion because it applies to tangential acceleration rather than translational deceleration. The correct approach involves using the torque equation τ = Iα, which accounts for the ball's moment of inertia and angular dynamics. Understanding the distinction between translational and tangential acceleration is crucial for solving such problems. Proper application of these concepts clarifies the relationship between friction, angular acceleration, and the motion of the bowling ball.
nahanksh
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Homework Statement


https://online-s.physics.uiuc.edu/cgi/courses/shell/common/showme.pl?courses/phys211/spring09/homework/10/bowling_ball/8.gif
A bowling ball 25 cm in diameter is slid down an alley with which it has a coefficient of sliding friction of µ = 0.6. The ball has an initial velocity of 11 m/s and no rotation. g = 9.81 m/s^2.
Given that the initial deceleration of the ball is 5.886.

What is the initial angular acceleration of the ball?



Homework Equations


For a sphere Icm = (2/5)mr^2.


The Attempt at a Solution



Firstly, i tried to use the formula \alpha = a/R
Then i got some value of acceleration which turns out to be wrong.

After that, when i used the torque equation \tau = I\alpha
I got the different answer and it was correct...

Why did i get the wrong answer at the first attempt?
I am really confused when i could use the transformation formulae(s to \theta, v to \omega, a to \alpha)...

Could someone help me out here..?
 
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When you used \alpha = a/R, I'm assuming the acceleration you used was the deceleration value they gave you. That value (the deceleration value) is the translational deceleration, meaning it is the deceleration of the center of mass of the ball. The equation you used is referring to the tangential acceleration of a point on the ball that is a radial distance R from some reference point (which you probably took as the center of mass).
 
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