Acceleration of Rest Point for Rolling without Slipping

In summary, the instantaneous acceleration vector of the rest point of a wheel rolling without slipping on a surface is always pointing toward the center of the wheel.
  • #1
0pt618
25
1
Let's ignore gravity in this problem for simplicity. For a wheel rolling without slipping on some surface, the rest point is the point at a given instant of time that is in contact with the surface (the rest point has zero instantaneous velocity). If the wheel is rolling at constant velocity, the instantaneous acceleration vector of the rest point points toward the center of the wheel.

Question: if the wheel is accelerating, in which direction is the instantaneous acceleration vector of the rest point?

(This is a question in the domain of classical mechanics, so all speeds are much less than the speed of light.)
 
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  • #2
Is this for schoolwork?
 
  • #3
berkeman said:
Is this for schoolwork?
No - why do you ask?
 
  • #4
Question edited to be more precise.
 
  • #5
Because we have rules here at the PF about how to handle schoolwork (you do the bulk of the work so we don't help you to cheat in your classes -- this applies to self-study as well). What is the context of your question? Is this for your work?
 
  • #6
berkeman said:
Because we have rules here at the PF about how to handle schoolwork (you do the bulk of the work so we don't help you to cheat in your classes -- this applies to self-study as well). What is the context of your question? Is this for your work?
Okay, makes sense. I read and learn physics for fun. It's not a homework problem.
 
  • #7
0pt618 said:
Okay, makes sense. I read and learn physics for fun. It's not a homework problem.
Okay, please post all schoolwork-type questions in the Homework Help forums, and fill out the HH Template that you are provided when you start a new thread there. That includes the Relevant Equations and your Attempt at a Solution. That helps you to organize your thoughts, and helps up to help you answer your question.

This thread is locked as a misplaced schoolwork type post. Please repost in HH Intro Physics.
 

Related to Acceleration of Rest Point for Rolling without Slipping

1. What is the definition of "Acceleration of Rest Point for Rolling without Slipping"?

The acceleration of rest point for rolling without slipping refers to the rate at which the rest point (the point on a rolling object that is in contact with the ground) accelerates while the object is rolling without slipping. This can also be thought of as the rate at which the object's velocity changes as it rolls without slipping.

2. How is the acceleration of rest point for rolling without slipping calculated?

The acceleration of rest point for rolling without slipping can be calculated using the equation a = rα, where a is the acceleration of the rest point, r is the radius of the object, and α is the angular acceleration. This equation is derived from the relationship between linear and angular acceleration, a = rω^2, where ω is the angular velocity.

3. What is the difference between "rolling without slipping" and "rolling with slipping"?

Rolling without slipping refers to a type of motion where an object is rolling and its point of contact with the ground is not sliding or slipping. This occurs when there is sufficient static friction between the object and the ground. In contrast, rolling with slipping refers to a type of motion where the point of contact between the object and the ground is slipping, resulting in a different type of acceleration and motion.

4. How does the acceleration of rest point for rolling without slipping affect an object's motion?

The acceleration of rest point for rolling without slipping affects an object's motion by determining its speed and direction of movement. Objects with a larger acceleration of rest point will have a greater change in velocity, resulting in a faster or more drastic change in motion. Additionally, the direction of the acceleration of rest point will determine the direction in which the object moves.

5. What factors can affect the acceleration of rest point for rolling without slipping?

The acceleration of rest point for rolling without slipping can be affected by a variety of factors, including the object's mass, the radius of the object, and the magnitude and direction of the applied force. Additionally, the coefficient of static friction between the object and the ground can also impact the acceleration of rest point, as this determines the amount of resistance against slipping. Other external factors such as the surface on which the object is rolling and air resistance can also play a role in the acceleration of rest point for rolling without slipping.

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