Basic non-rotating accelerating reference frame problem

In summary, the problem involves a uniform thin rod of length L and mass M pivoted at one end and attached to a car accelerating at a rate A. The goal is to find the equilibrium value of the angle theta between the rod and the top of the car. After considering the acceleration of the car as a horizontal gravitational field and using torque balance, the two forces cancel out and the solution is found.
  • #1
MuIotaTau
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Homework Statement



A uniform thin rod of length ##L## and mass ##M## is pivoted at one end. The pivot is attached to the top of a car accelerating at rate ##A##. What is the equilibrium value of the angle ##\theta## between the rod and the top of the car?

Homework Equations



None in particular?

The Attempt at a Solution



I understand that we can treat the acceleration of the car as a horizontal gravitational field of strength ##A##. I attempted to solve the problem via torque balance (taking the torque about the pivot), but the only two forces, gravity and the fictional force, have ##\theta## terms that end up cancelling out. I'm sure this is simple, but honestly moving on is going to problem if I can't even do this problem, haha.
 
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  • #2
Oh, never mind, totally figured this one out.
 

FAQ: Basic non-rotating accelerating reference frame problem

1. What is a non-rotating accelerating reference frame problem?

A non-rotating accelerating reference frame problem is a physics concept that involves a reference frame that is both non-rotating (not spinning) and accelerating (changing its velocity). In this scenario, objects within the reference frame experience fictitious forces, such as the centrifugal force, due to the acceleration.

2. How is a non-rotating accelerating reference frame problem different from a rotating reference frame problem?

In a rotating reference frame, objects experience centrifugal and Coriolis forces due to the rotation of the frame. However, in a non-rotating accelerating reference frame, objects only experience fictitious forces due to the acceleration of the frame. The key difference is that in the non-rotating case, the frame itself is not rotating, but is instead accelerating.

3. What are some real-life examples of non-rotating accelerating reference frame problems?

One example is a car taking a sharp turn. The passengers in the car will experience a centrifugal force pushing them towards the outside of the turn, even though the car itself is not rotating. Another example is a rollercoaster going over a loop. The riders will experience a force pushing them towards the outside of the loop, even though the rollercoaster is not rotating.

4. How do you solve a basic non-rotating accelerating reference frame problem?

To solve a basic non-rotating accelerating reference frame problem, you need to first identify the frame of reference and the acceleration of that frame. Then, you can use Newton's laws of motion and the equations for fictitious forces to analyze the motion of objects within that frame. It is also important to keep track of the direction and magnitude of the fictitious forces, as they can affect the overall motion of the objects.

5. What are the practical applications of understanding non-rotating accelerating reference frame problems?

Understanding non-rotating accelerating reference frame problems is essential in many fields, such as engineering, aviation, and space travel. It allows us to accurately predict and account for the effects of acceleration on objects, which is crucial for designing safe and efficient systems and vehicles. It also helps us understand and explain various phenomena, such as the feeling of being pushed against your seat during takeoff in an airplane.

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