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

• nahanksh
In summary: Since the tangential acceleration is related to the translational acceleration by the distance from the center of mass, it will not give you the correct answer. The correct equation to use here is \alpha = a/r, where r is the radius of the ball. This will give you the correct answer because the tangential acceleration is related to the translational acceleration by the radius of the ball, not the distance from the center of mass. In summary, the initial angular acceleration of the bowling ball can be found using the equation \alpha = a/r, where a is the deceleration of the ball and r is the radius of the ball. Using the formula \tau = I\alpha, where I is the moment of inertia
nahanksh

## 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..?

Last edited by a moderator:
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).

Last edited:

I would like to point out that rotational kinematics can be a complex topic and it is not uncommon to make mistakes in calculations. In this particular scenario, it is important to note that the bowling ball is sliding down the alley, which means that both translational and rotational motion are occurring simultaneously. This means that the equations used for purely rotational motion may not accurately represent the situation.

In your first attempt, you used the formula \alpha = a/R, which is correct for a point rotating around a fixed axis. However, in this case, the ball is not rotating around a fixed axis, but rather it is sliding and rotating at the same time. This means that the radius of rotation is constantly changing, making this formula not applicable.

In your second attempt, you used the torque equation \tau = I\alpha, which is the correct approach for this scenario. This equation takes into account both the translational motion (through torque) and the rotational motion (through moment of inertia). This is why you got the correct answer using this equation.

It is also important to note that in rotational kinematics, we use different variables and equations compared to translational motion. When dealing with rotational motion, we use angular displacement (\theta), angular velocity (\omega), and angular acceleration (\alpha), while in translational motion we use linear displacement (s), linear velocity (v), and linear acceleration (a). This is because rotational motion involves circular motion, which has its own unique set of equations.

In conclusion, it is crucial to carefully consider the scenario and choose the appropriate equations when dealing with rotational kinematics. It is also important to understand the differences between rotational and translational motion and use the correct variables and equations accordingly.

## 1. What is rotational kinematics?

Rotational kinematics is the study of the motion of objects as they rotate around a fixed axis. It involves the measurement and calculation of various quantities such as angular velocity, angular acceleration, and rotational displacement.

## 2. How is rotational kinematics different from linear kinematics?

Rotational kinematics is concerned with the motion of objects as they rotate, while linear kinematics deals with the motion of objects in a straight line. Rotational kinematics involves different quantities and equations, such as angular displacement and moment of inertia, compared to linear kinematics.

## 3. What is angular velocity in rotational kinematics?

Angular velocity is the rate of change of angular displacement over time. It is measured in radians per second and represents how quickly an object is rotating around a fixed axis.

## 4. How does torque affect rotational kinematics?

Torque is a measure of the force that causes an object to rotate. In rotational kinematics, torque can change an object's angular velocity and angular acceleration, and can also cause an object to rotate around a fixed axis.

## 5. What is the difference between angular displacement and linear displacement?

Angular displacement is a measure of how much an object has rotated around an axis, while linear displacement is a measure of how far an object has moved in a straight line. They are both measured in different units and represent different types of motion.

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