Particle on a Circle Homework: Solving with Newton's Law

In summary, the conversation discusses the forces and acceleration acting on a particle sliding on a big sphere. The main focus is on the weight and centripetal acceleration, with the question of whether the force of weight should be exceeded by the centripetal acceleration. The conversation also mentions the need for a variable to denote the particle's position and the speed and acceleration at a given angle.
  • #1
faen
140
0

Homework Statement


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Homework Equations



I suppose Newtons third and second law.

centripetal acceleration = v^2 /R

The Attempt at a Solution



I'm thinking that the force due to weight, should be exceeded by the centripetal acceleration?

I couldn't get the calculations to add up though. Anyone know how to solve it or if I'm on the right track at all? Thanks for any help! :)
 
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  • #2
What forces act on the particle when sliding on the big sphere, and in what directions?

ehild
 
  • #3
The weight acts perpendicular to the circle, and movement acts parallel to the circle.
 
  • #4
I think you are on the right track. "I'm thinking that the force due to weight, should be exceeded by the centripetal acceleration?"
Consider the forces acting normal to the surface of the sphere where the particle leaves the sphere.
 
  • #5
faen said:
The weight acts perpendicular to the circle, and movement acts parallel to the circle.
No, weight is due to gravity, so always acts vertically, and movement is not a force.
There is a force perpendicular to the arc of the circle. What is it usually called and where does it come from?
You need a variable to denote the particle's position at an arbitrary point. You could use the height it has descended so far, but the angle of arc it has traveled will be more convenient. What will be its speed when at angle theta? What will be its acceleration if it is remaining in contact with the circle?
 

FAQ: Particle on a Circle Homework: Solving with Newton's Law

What is a particle on a circle?

A particle on a circle refers to a physical system where a point particle moves along the circumference of a circle under the influence of a force.

What is Newton's Law for a particle on a circle?

Newton's Law for a particle on a circle states that the sum of the forces acting on the particle must be equal to its mass multiplied by its acceleration in the tangential direction.

How do you solve for the motion of a particle on a circle using Newton's Law?

To solve for the motion of a particle on a circle using Newton's Law, you must first identify all the forces acting on the particle, including the centripetal force. Then, you can use Newton's Second Law to set up an equation and solve for the acceleration. Finally, you can integrate the acceleration to find the particle's position and velocity as a function of time.

What is the centripetal force in a particle on a circle?

The centripetal force is the force that acts towards the center of the circle, keeping the particle in its circular motion. It is equal to the mass of the particle multiplied by its tangential acceleration.

What are some common applications of particle on a circle problems?

Particle on a circle problems can be found in many real-life scenarios, such as the motion of planets around the sun, the motion of a car around a circular track, and the motion of a rollercoaster on a loop. They are also commonly used in physics experiments and simulations to understand and analyze circular motion.

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