# Slipping transitioning to rolling without slipping

• lightofthemoon
In summary, the conversation discusses solving a physics problem involving a solid spherical ball being thrown onto a horizontal surface with a given mass, radius, and initial conditions. The problem involves finding the value of the coefficient of kinetic friction and using conservation of energy and forces to solve for the initial velocity and angular velocity of the ball. The expert suggests using angular impulse as the most straightforward approach to solving the problem.
lightofthemoon

## Homework Statement

A solid spherical ball of mass 0.75 kg and radius 5.0 cm is thrown onto a horizontal surface with coefficient of kinetic friction μ . It’s initial velocity at time t = 0 is horizontal and its initial angular velocity is zero. After rolling with slipping for a time t1 = 0.76 seconds, the ball begins to roll without slipping with angular speed ω1 = 120 rad/s. It continues to roll without slipping up a short ramp of height h = 16 cm

What is the value of μ?

## Homework Equations

KE = .5mv^2 = 5Iω^2
f= μN
T=Fr=Iα
vf=vi +at

## The Attempt at a Solution

I was thinking about solving this problem with conservation of energy.
.5mv^2 + .5Iω^2 - μmgd = .5mv^2 + .5Iω^2
However, we don't know the initial velocity, or the distance that the ball traveled with slipping.
In order to solve for initial velocity I thought about using one of the four kinematic equations. However, for each of the equations where are at least 2 unknowns.

So I also tried using forces to solve this problem as well.
Acceleration due to friction
f= μN
ma= μN
a=μg
Rotational acceleration
T=Fr=Iα
α= 5μg / 2r
Then I'd use the equation vf=vi +at and it's rotational equivalent. But this is where I'm stuck again, because there are also 2 unknown variables.

Since you're given the time, try using impulse.

I don't really understand.
Impulse= change in momentum = Ft
momentum = mv, so don't I still have to find the initial velocity as well as μ?

Consider angular impulse.

Oh, I see how to do the problem
But why don't I have to consider linear impulse as well since the ball is also traveling linearly?

lightofthemoon said:
Oh, I see how to do the problem
Good!

lightofthemoon said:
But why don't I have to consider linear impulse as well since the ball is also traveling linearly?
Since you happen to be given the initial and final angular speed of the ball, using angular impulse is the most straightforward approach. And it's all you need. (You can then calculate the initial velocity, if you like.)

Oh, ok. Thanks for your help!

## 1. What is the difference between slipping and rolling without slipping?

Slipping is when an object is moving and its point of contact with the ground is not stationary. Rolling without slipping is when an object is moving and its point of contact with the ground is stationary.

## 2. Why is it important to understand slipping transitioning to rolling without slipping?

Understanding slipping transitioning to rolling without slipping is important in many real-world situations, such as designing tires for vehicles or predicting the motion of objects in sports or engineering.

## 3. What factors affect the transition from slipping to rolling without slipping?

The main factors that affect this transition are the coefficient of friction between the object and the ground, the object's mass, and the object's rotational inertia.

## 4. How can we calculate the point at which an object transitions from slipping to rolling without slipping?

The critical point at which an object transitions from slipping to rolling without slipping can be calculated using the equation μ = rω^2, where μ is the coefficient of friction, r is the radius of the object, and ω is the angular velocity.

## 5. What are some real-world examples of slipping transitioning to rolling without slipping?

Some common examples include rolling a ball on a surface, driving a car, or riding a bike. In all of these situations, the object experiences a transition from slipping to rolling without slipping as it gains traction and the point of contact with the ground becomes stationary.

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