Solving Turntable Coin Problem: Angular & Linear Accelerations

In summary, a coin is placed 10.5 cm away from the spindle of a turntable that starts spinning with constant angular acceleration from rest. After 0.133 s, the coin's centripetal acceleration is 1.39 times its tangential acceleration. To find the turntable's angular acceleration, we need to use the formula a_c = ω^2 * r, where a_c is the centripetal acceleration, ω is the angular velocity, and r is the distance from the center. To find the angle by which the turntable turns in 0.133 s, we can use the formula θ = ω * t, where θ is the angle, ω is the angular
  • #1
Nick11111
1
0
A very small coin is at distance 10.5 cm from the spindle of a turntable. The turntable starts spinning from rest with constant angular acceleration. In 0.133 s the coin's centripetal acceleration is 1.39 times its tangential acceleration.
1)Find the turntable's angular acceleration.
2)Find the angle by which the turntable turns in 0.133 s.
3)Find the magnitude of the coin's linear acceleration in 0.133 s.

Having trouble please help
 
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  • #2
Hello Nick, welcome to PF :smile: !

So far for the problem statement. Interesting.

Now for the rest of the template. The guidelines require an effort on your part to come to a solution. That also helps us to provide more useful assistance: you don't need the answer, you need the exercise !

Homework Equations

[/B] -- check here

The Attempt at a Solution

[/B]-- think what you would do with linear motion and try to translate to rotation
 

1. What is the "Turntable Coin Problem"?

The Turntable Coin Problem is a classic physics problem that involves a turntable with a coin placed at its center. The turntable starts at rest and gradually accelerates, causing the coin to slide towards the edge of the turntable. The aim is to determine the speed of the turntable at which the coin will slide off the edge.

2. How do angular and linear accelerations play a role in this problem?

Angular acceleration refers to the rate at which the turntable's rotational speed changes, while linear acceleration refers to the rate at which the coin's distance from the center increases. In the Turntable Coin Problem, the angular acceleration of the turntable causes a linear acceleration of the coin towards the edge.

3. What are the key equations used to solve this problem?

The key equations used to solve the Turntable Coin Problem are Newton's Second Law of Motion, which states that force equals mass times acceleration, and the centripetal acceleration formula, which relates the angular and linear accelerations of an object moving in a circular path.

4. Can this problem be solved analytically or does it require numerical methods?

This problem can be solved analytically by using the equations mentioned above and manipulating them to solve for the unknown variables. However, in some cases, numerical methods may be required to find a precise solution due to the complexity of the equations.

5. What are some real-world applications of the Turntable Coin Problem?

The Turntable Coin Problem has various applications in physics, engineering, and technology. For example, it can be used to study the motion of satellites and planets, as well as the stability of rotating machinery. It also has practical applications in designing amusement park rides and calculating the maximum speed at which a car can make a turn without tipping over.

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