Rolling as Translation and Rotation Combined

In summary, the question asks for the magnitude of the angular acceleration of an automobile's tires, given its initial angular speed and the number of complete turns it takes for it to come to a stop without skidding. The formula used to solve this is (ω^2 - ωi^2)/(2 * change in theta), where ωi is the initial angular speed. The resulting answer is 2.038 rad/s^2, which is slower than the initial angular speed of 19.6 rad/s.
  • #1
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Homework Statement


An automobile traveling at 30.0 km/h has tires of 85.0 cm diameter.

(b) If the car is brought to a stop uniformly in 15.0 complete turns of the tires (without skidding), what is the magnitude of the angular acceleration of the wheels?

(In part a I found the angular speed to be 19.6 rad/s



Homework Equations



(w^2 - wi^2)/(2 * change in theta) ??

The Attempt at a Solution



-wi^2/(2 *(2* 15pi) = angular acceleration

I'm super lost and would appreciate any help at all. I just need a pointer in the right direction!
 
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  • #2
Your formula is correct. Check your ωi.
 
  • #3
I know that my wi is correct though..
Is there another way to solve this problem maybe?
 
  • #4
Well, would the answer 2.038rad/s^2 make sense?
Because that's what I got for my answer but I wasn't expecting the acceleration to be that much slower than the speed
 
  • #5
Your answer is correct.
 
  • #6
Ok thank you so much!
 

1. What is rolling as translation and rotation combined?

Rolling as translation and rotation combined, also known as combined rolling motion, is a type of motion where an object moves along a surface while also rotating about its own axis. This is commonly seen in rolling objects such as wheels or balls.

2. How is rolling as translation and rotation combined different from regular rolling?

In regular rolling, the object only moves along the surface without any rotation about its own axis. However, in combined rolling motion, the object also rotates about its axis while moving along the surface.

3. What is the significance of studying rolling as translation and rotation combined?

Studying combined rolling motion is important in understanding the physics of objects in motion. It helps us understand the relationship between translation and rotation, and how these motions can affect an object's speed, direction, and stability.

4. Can an object have combined rolling motion on any surface?

No, an object can only have combined rolling motion on surfaces with sufficient friction. This is because the friction force is what allows the object to both move and rotate.

5. How is combined rolling motion used in real life?

Combined rolling motion is used in various applications such as in transportation (e.g. car wheels, bicycle wheels), sports (e.g. balls, wheels on skates), and machinery (e.g. gears, pulleys). Understanding this type of motion is also important in designing and optimizing these objects for their intended use.

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