Equilibrium value of an angle

In summary, a uniform thin rod of length L and mass M is pivoted at one end and attached to the top of a car accelerating at a rate A. The equilibrium value of the angle \Theta between the rod and the car can be found by setting the fictional force equal to the force of weight and solving for theta using Newton's second law. For part B, the motion of the rod for small angles \Phi from equilibrium would be towards equilibrium, with the vertical component of motion remaining the same due to the approximation cos\Phi=1.
  • #1
davesface
97
2
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.

a.) What is the equilibrium value of the angle [tex]\Theta[/tex] between the rod and the top of the car?

Honestly, I'm not entirely sure what the question even wants me to find. Playing the problem out in my mind, it seems like the angle would just continue to increase at a constant rate as the car accelerates with a constant rate A, but clearly this is not the case.

b.) Suppose that the rod is displaced a small angle [tex]\Phi[/tex] from equilibrium. What is its motion for small [tex]\Phi[/tex]?

I would assume that the motion would be towards equilibrium, although the vertical component of motion for the rod itself should still be the same, as the approximation cos[tex]\Phi[/tex]=1 should hold for small values of [tex]\Phi[/tex].
 
Physics news on Phys.org
  • #2
Hi davesface! :smile:

Let's do a.) first …
davesface said:
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.

a.) What is the equilibrium value of the angle [tex]\Theta[/tex] between the rod and the top of the car?

Hint: in equilibrium, the acceleration of the end of the rod will be the same as the acceleration of the car.

So use good ol' Newton's second law :smile:
 
  • #3
OK, part A was a lot easier than I thought, and all I did was set the fictional force backwards equal to the force of weight and solve for theta.

Turns out that part B would've required us to solve a differential equation, which no one knows how to do. Thanks for the response, though.
 

What is the equilibrium value of an angle?

The equilibrium value of an angle is the angle at which the forces acting on an object are balanced, resulting in a state of equilibrium. This means that the object will remain at rest or in a constant motion at this angle.

How is the equilibrium value of an angle calculated?

The equilibrium value of an angle can be calculated using the principles of torque and moments. The net torque acting on an object must be equal to zero for it to be in equilibrium. By setting up an equation with the forces and distances involved, the equilibrium value of the angle can be determined.

What factors affect the equilibrium value of an angle?

The equilibrium value of an angle is affected by the forces acting on the object, the distance of these forces from the pivot point, and the mass and distribution of mass of the object. Any changes in these factors can alter the equilibrium value of the angle.

What is the significance of the equilibrium value of an angle?

The equilibrium value of an angle is important in understanding the stability and balance of objects. It is also crucial in engineering and design, as it helps determine the most efficient and safe angles for structures and machines to maintain equilibrium.

Can the equilibrium value of an angle change?

Yes, the equilibrium value of an angle can change if any of the factors affecting it are altered. For example, if the forces acting on the object increase, the equilibrium value of the angle may shift to a different value in order to maintain balance.

Similar threads

  • Introductory Physics Homework Help
Replies
31
Views
947
  • Introductory Physics Homework Help
Replies
7
Views
2K
  • Introductory Physics Homework Help
Replies
13
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
2K
  • Introductory Physics Homework Help
5
Replies
157
Views
6K
  • Introductory Physics Homework Help
Replies
4
Views
7K
  • Classical Physics
2
Replies
47
Views
2K
  • Introductory Physics Homework Help
Replies
32
Views
962
  • Introductory Physics Homework Help
Replies
15
Views
2K
  • Introductory Physics Homework Help
Replies
1
Views
640
Back
Top