Coin Rolling Without Slipping: Physics Final Study Question

In summary, a coin with a diameter of 2.30 cm and an initial angular speed of 18.4 rad/s is dropped onto a horizontal surface and rolls without slipping. With an angular acceleration of 2.17 rad/s2, the coin eventually comes to rest. To find the distance the coin rolls, the formula vf2 = vi2 + 2aΔx can be used, where α is the angular acceleration and Δθ can be found by dividing both sides by the coin's radius squared and multiplying by R.
  • #1
mattmets
2
0
A coin with a diameter of 2.30 cm is dropped onto a horizontal surface. The coin starts out with an initial angular speed of 18.4 rad/s and rolls in a straight line without slipping. If the rotation slows with an angular acceleration of magnitude 2.17 rad/s2, how far does the coin roll before coming to rest?


Can anyone help- I'm trying to study for a physics final and I'm getting nowhere! Thanks.
 
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  • #2
Unless I'm missing something here, you can use this formula:

vf2 = vi2 + 2aΔx

Dividing both sides by R2, the coin's radius squared, we get:

ωf2 = ωi2 + 2αΔθ

Where α is the coin's angular acceleration, which is negative in this case. From here you can find Δθ and multiplying by R you can find the total distance traveled by the coin.
 
Last edited:
  • #3
Great...thanks :biggrin:
 

Related to Coin Rolling Without Slipping: Physics Final Study Question

1. What is the concept of rolling without slipping?

The concept of rolling without slipping is when a coin, or any object, rolls along a surface without sliding or slipping. This means that the point of contact between the coin and the surface is always at rest, while the rest of the coin is in motion.

2. How does friction play a role in coin rolling without slipping?

Friction is essential in allowing an object to roll without slipping. It provides the necessary force to keep the point of contact at rest while the rest of the object is in motion. Without friction, the object would simply slide or slip instead of rolling.

3. What are the factors that affect the rolling without slipping motion?

The factors that affect the rolling without slipping motion are the mass and shape of the object, the surface it is rolling on, and the force of friction. The larger the mass and more uneven the surface, the more force is needed to maintain rolling without slipping.

4. How is the angular velocity of a rolling coin related to its linear velocity?

The angular velocity of a rolling coin is directly related to its linear velocity. This means that as the angular velocity increases, so does the linear velocity. This is because the two velocities are linked by the radius of the coin, which remains constant in a rolling motion.

5. Can an object ever roll without slipping on a perfectly smooth surface?

No, it is not possible for an object to roll without slipping on a perfectly smooth surface. This is because there would be no friction present to provide the necessary force to keep the point of contact at rest. Without friction, the object would simply slide or slip instead of rolling.

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