Solving a Coin Drop Problem - Need Help

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In summary, the problem involves a coin with a diameter of 2.4 cm and an initial angular speed of 18 rad/s being dropped on edge onto a horizontal surface. The coin rolls without slipping and slows down with an angular acceleration of 1.9 rad/s^2. The goal is to determine the distance the coin rolls before coming to rest. One method is to calculate the time it takes for the coin to stop, using the definition of angular acceleration. Another method is to use the kinematic formula relating angular distance and speed. Both methods were suggested by the participants in the conversation.
  • #1
doxigywlz
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Okay, I have this very EASY question (or so it appears) but I don't know how to figure out the time in this problem:

a coin with a diameter of 2.4 cm is dropped on edge onto a horizontal surface. the coin starts out with an initial angular speed of 18 rad/s and rolls in a straight line without slipping. if the rotation slows with an angular acceleration of magnitude 1.9 rad/s^2, how far does the coin roll before coming to rest?

I know w initial is 18 rad/s and w final is 0
alpha is 1.9rad/s^2 (or is it negative??)
we're looking for theta...

I could figure it out if I had the time.. Can someone help me out?? Thanks
 
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  • #2
doxigywlz said:
I could figure it out if I had the time..
That's one way to do it. So figure out the time. Hint: What's the definition of acceleration?
 
  • #3
I'm going to guess here...
Since v = rw, r = 2.4/2 = 1.2, and w = 18rads^-1, so 18(1.2) = v (Not going to calculate, too lazy and tired..)
a = Ar, and A = 1.9rads^-2, r = 1.2, so a = 1.9(1.2)...
Now, we'll consider v to be initial velocity, u...
Use the formula:
v^2 = u^2 + 2as
Where s = distance, plug it in..
0^2 = (18(1.2))^2 + 2(1.9(1.2))s
And solve for s.
I hope I gave the right method, tell me if it worked. :-\
 
  • #4
pseudo, no-- it didn't work (unless I did it wrong)...

Acceleration is meters per second squared or, in this case, radians per second squared... so how does that help me solve for time?
1.9=change in w over seconds squared.. i tried to solve for it, but i got it wrong..

please a little more help? i have to go to work now but i will definitely check back later
 
  • #5
Hmmm, I seem to have made a mistake writing that...
Change the acceleration to a negative value, thus giving the equation:
0^2 = (18(1.2))^2 + 2(-1.9(1.2))s
Try solving for s now and see if it works.
There's no way it's going to come to rest if it's not deceleration! (Unless I haven't learned about something in Physics which causes something to come to rest, rather than net forces..)
 
  • #6
doxigywlz said:
Acceleration is meters per second squared or, in this case, radians per second squared... so how does that help me solve for time?
1.9=change in w over seconds squared.. i tried to solve for it, but i got it wrong..
The definition of angular acceleration is change of angular velocity (omega) per unit time. Writing it for rotational motion: [itex]\alpha = \Delta \omega / \Delta t[/itex]. You know the change in [itex]\omega[/itex] and the acceleration, so find the time.

By the way, Pseudo Statistic just solved the problem slightly differently. (That's why in my first response I said that your way is just one way of solving for the angle.) I recommend that you solve the problem both ways, just for the practice. Your way: find the time, then use it to find the distance. His way: Use the kinematic formula relating angular distance and speed to get the answer directly. (For some reason Pseudo Statistic converted from angular to linear speed in writing the kinematic equation--that's not wrong, just unnecessary. Also, as he realized, he made a slight error in signs. In any case, the kinematic equation he used is: [itex]\omega_f^2 = \omega_i^2 + 2\alpha \theta[/itex].)
 
  • #7
Doc Al said:
The definition of angular acceleration is change of angular velocity (omega) per unit time. Writing it for rotational motion: [itex]\alpha = \Delta \omega / \Delta t[/itex]. You know the change in [itex]\omega[/itex] and the acceleration, so find the time.

By the way, Pseudo Statistic just solved the problem slightly differently. (That's why in my first response I said that your way is just one way of solving for the angle.) I recommend that you solve the problem both ways, just for the practice. Your way: find the time, then use it to find the distance. His way: Use the kinematic formula relating angular distance and speed to get the answer directly. (For some reason Pseudo Statistic converted from angular to linear speed in writing the kinematic equation--that's not wrong, just unnecessary. Also, as he realized, he made a slight error in signs. In any case, the kinematic equation he used is: [itex]\omega_f^2 = \omega_i^2 + 2\alpha \theta[/itex].)
Hey, atleast I got it right. ;)
We aren't even going to take Angular velocity/acceleration in the Physics course I'm in. :(
 

1. How do I solve a coin drop problem?

To solve a coin drop problem, you first need to define the parameters of the problem, such as the height of the coin drop, the number of coins, and the surface the coins are dropping onto. Then, you can use mathematical equations and principles, such as the laws of motion and energy conservation, to calculate the outcome.

2. What is the best strategy for solving a coin drop problem?

The best strategy for solving a coin drop problem may vary depending on the specific problem, but some general tips include breaking down the problem into smaller parts, using visual aids such as diagrams or graphs, and double-checking your calculations for accuracy.

3. What are some common mistakes to avoid when solving a coin drop problem?

Some common mistakes to avoid when solving a coin drop problem include forgetting to consider factors such as air resistance, neglecting to convert units when necessary, and overlooking key details in the problem statement. It's also important to check your calculations and assumptions carefully to prevent errors.

4. Can a coin drop problem be solved using a computer program or simulation?

Yes, a coin drop problem can be solved using a computer program or simulation. This can be a helpful tool for checking your manual calculations and visualizing the problem. However, it's important to remember that the results from a simulation may not always be 100% accurate and should be used as a supplement to manual calculations.

5. What are some real-world applications of solving coin drop problems?

Solving coin drop problems has many real-world applications, such as in engineering, physics, and game design. For example, understanding the physics behind a coin drop can help engineers design more efficient airbags in cars or improve the accuracy of coin-operated machines. It can also be used in game design to create realistic physics in virtual simulations.

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