# Solving Rolling Bowling Ball Problem: Motion & Friction

• labgoggles
In summary, the problem involves a bowler throwing a bowling ball of radius R= 11 cm with initial speed vcom = 8.5 m/s and initial angular speed w0 = 0 along a lane with a coefficient of kinetic friction of 0.21. The ball experiences linear and angular acceleration until it stops sliding and starts rolling smoothly. The time it takes for the ball to transition from sliding to rolling can be calculated using conservation of energy or angular momentum.
labgoggles
Hi everyone, this problem involves smooth rolling and translational motion:

1. Homework Statement

A bowler throws a bowling ball of radius R= 11 cm along a lane. The ball slides on the lane with initial speed vcom = 8.5 m/s and initial angular speed w0 = 0. The coefficient of kinetic friction between the ball and the lane is 0.21. The kinetic frictional force acting on the ball causes a linear acceleration of the ball while producing a torque that causes and angular acceleration of the ball. When speed vcom has decreased enough and angular speed w has increased enough, the ball stops sliding and then rolls smoothly. d)how long does the ball slide?

## Homework Equations

Flinear = ma = -mgμk
torque = rF = Iα
Ki + Ui = Kf + Uf

## The Attempt at a Solution

I have figured out the linear acceleration a = -2.1 m/s2, and angular acceleration α = 47 rad/s2 using the fact that Flinear = ma = -mgμk and torque = rF = Iα.

I know that there is smooth rolling if vcom = rω = (.11m)ω

I set up an equation using conservation of energy to solve for ωf, which is whenvsliding should end and smooth rolling should begin.

(1/2)mvi2 + (1/2)I ωi2 = (1/2)mvf2 + (1/2) I ωf2

(1/2)m(8.5m/s)2 = (1/2)m(.11ω)2 + (1/2)(2/5 mr2f2

Canceling out mass and simplifying:

36.125 m2/s2 = .00605ω2 + .00242ω2

then, ω = ω0 + αt

t= 1.4 s

However, the given answer in the book is 1.2s, and I'm not sure what's going on...I've tried to account for rounding errors, but that doesn't appear to be the problem. Am I neglecting friction when I shouldn't be, and if so, how would I calculate energy lost to friction if I don't yet know the distance the ball traveled? Any help would be appreciated, thank you.

Are you sure conservation of energy applies here ?

With sliding friction, there is work being done that goes away as heat.

Since you've calculated the linear deceleration and angular acceleration, how long does it take before the ball transitions from sliding into rolling motion?

labgoggles said:
linear acceleration a = -2.1 m/s2,
Are you taking g as 10 m/s2? Given the precision of the other data, I would use 9.8.
But the most important thing is to follow rcgldr's hint and not assume work is conserved.

By the way, if you only wanted the final velocity and didn't care about the distance or time to that point, a neat trick is to consider conservation of angular momentum. You have to choose the reference axis carefully so that friction can be ignored.

Thank you! I was able to get the answer using conservation of momentum: rmvi = rmvf + Iω. But what is the deal with rmv, and why wouldn't I use just mv for translational momentum? As in, what is the difference between the two types of momentum in this equation I set up? I know it's correct, but I'm not sure why...

You didn't need to use conservation of momentum either. The friction force divided by the mass of the ball is the linear deceleration of the ball, and the friction force times the radius of the ball divided by the angular inertia of the ball is the angular acceleration of the ball. This allows you to calculate the linear speed (which is decreasing) of the ball versus time, and the surface speed of the ball (which is increasing): radius x ω versus time, and at some point in time they are equal and the ball transitions into rolling.

Last edited:
labgoggles said:
Thank you! I was able to get the answer using conservation of momentum: rmvi = rmvf + Iω. But what is the deal with rmv, and why wouldn't I use just mv for translational momentum? As in, what is the difference between the two types of momentum in this equation I set up? I know it's correct, but I'm not sure why...
The frictional force contributes a change to the horizontal linear momentum. It can be omitted from the angular momentum equation by taking the axis to be a point in the line of action of the frictional force. The friction doesn't matter then because it has no moment about the axis.

## 1. What is the rolling bowling ball problem?

The rolling bowling ball problem is a physics problem that involves determining the motion of a bowling ball as it rolls down a lane. This problem takes into account factors such as friction and the shape of the ball to predict its final position and speed.

## 2. How does friction affect the motion of a rolling bowling ball?

Friction is a force that resists motion between two surfaces. In the case of a rolling bowling ball, friction acts in the opposite direction of the ball's motion and causes it to slow down. The amount of friction depends on factors such as the surface of the lane and the weight of the ball.

## 3. What are the different types of friction involved in the rolling bowling ball problem?

There are two types of friction involved in the rolling bowling ball problem: static friction and kinetic friction. Static friction occurs when the ball is not moving, and kinetic friction occurs when the ball is in motion. Both types of friction play a role in the ball's motion down the lane.

## 4. How can the motion of a rolling bowling ball be calculated?

The motion of a rolling bowling ball can be calculated using Newton's laws of motion and the principles of rotational motion. This involves considering the forces acting on the ball, such as gravity and friction, and using equations to determine its velocity and position at different points along the lane.

## 5. How can the rolling bowling ball problem be solved in real-world scenarios?

In real-world scenarios, the rolling bowling ball problem can be solved by taking into account additional factors such as air resistance and the imperfections of the lane surface. Advanced techniques such as computer simulations and experimental data can also be used to improve the accuracy of the solution.

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