# How Does Friction Affect Particle Motion in Circular Dynamics?

• joemama69
In summary, a particle of mass m moves in a horizontal circle of radius R on a rough table and is attached to a horizontal string fixed at the center of the circle. The speed of the particle is initially v0 and after one full trip around the circle, it is v0/2. The energy dissipated by friction during one revolution can be found using the equation .5Iwo2 = 1/8Iwo2 + Wfriction, where Wfriction is equal to 3/8Iwo2. The coefficient of kinetic friction can be found by solving for u in the equation umg = Wfriction. The number of revolutions the particle will make before coming to rest can be found by solving
joemama69

## Homework Statement

A particle of mass m moves in a horizontal circle of radius R on a rough table. It is attached to a horizontal string fixed at the center of the circle. The speed of the particle is initially v0. After completing one full trip around the circle, the speed of the particle is v0/2.

a) Find the energy dissipated by friction during one revolution in terms of m, v0, and R.

b) What is the coefficient of kinetic friction?

c) How many revolutions will the particle make before coming to rest?

d) Suppose the experiment is repeated with one slight modification: the initial speed of the particle is doubled. How many revolutions does the particle make in this case?

## The Attempt at a Solution

I need some help withthe friction part

.5Iwo2 = .5Iw2 - Friction energy

is the friction energy F = umg

.5Iwo2 = .5Iw2 - umg

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joemama69 said:
I need some help withthe friction part

.5Iwo2 = .5Iw2 - Friction energy

is the friction energy F = umg

.5Iwo2 = .5Iw2 - umg

umg would be the force. Work done is W=Fd.

part a)

so the energy would be .5Iwo2 = 1/8Iwo2 + Wfriction... at one rotation it is half the velocity

Wf = 3/8Iwo2

is this the energy dissipated

Last edited:
and for part b i use umgRQ. where Q is theta in radians as the Work of friction

and then i would solve it for u.

and part c i just solve for RQ

part d i would just double initial velocity and solve for RQ again

should i be solveing for RQ because of the distance it travels around teh circle, or should the answer be in simply Q in radians

## 1. What is circular motion with friction?

Circular motion with friction is the movement of an object in a circular path while experiencing frictional forces, which oppose the motion of the object. This type of motion is commonly seen in objects such as car tires, amusement park rides, and planets orbiting around the sun.

## 2. What causes circular motion with friction?

Circular motion with friction is caused by the combination of a centripetal force and a frictional force. The centripetal force is responsible for keeping the object moving in a circular path, while the frictional force acts in the opposite direction, slowing down the object's motion.

## 3. How does friction affect circular motion?

Friction affects circular motion by reducing the speed of the object and changing its direction. This is because frictional forces act against the direction of motion, causing the object to slow down and eventually come to a stop if the frictional force is greater than the centripetal force.

## 4. Can circular motion with friction be beneficial?

Yes, circular motion with friction can be beneficial in certain situations. For example, the frictional force between car tires and the road allows for better traction and control while driving. On amusement park rides, friction is used to control the speed and direction of the ride, making it more enjoyable and safe for riders.

## 5. How can circular motion with friction be calculated?

Circular motion with friction can be calculated using the equations of circular motion, which take into account the frictional force and the centripetal force. These equations can be solved to find the speed, acceleration, and radius of the circular path of the object.

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