Rolling is a type of motion that combines rotation (commonly, of an axially symmetric object) and translation of that object with respect to a surface (either one or the other moves), such that, if ideal conditions exist, the two are in contact with each other without sliding.
Rolling where there is no sliding is referred to as pure rolling. By definition, there is no sliding when there is a frame of reference in which all points of contact on the rolling object have the same velocity as their counterparts on the surface on which the object rolls; in particular, for a frame of reference in which the rolling plane is at rest (see animation), the instantaneous velocity of all the points of contact (e.g., a generating line segment of a cylinder) of the rolling object is zero.
In practice, due to small deformations near the contact area, some sliding and energy dissipation occurs. Nevertheless, the resulting rolling resistance is much lower than sliding friction, and thus, rolling objects, typically require much less energy to be moved than sliding ones. As a result, such objects will more easily move, if they experience a force with a component along the surface, for instance gravity on a tilted surface, wind, pushing, pulling, or torque from an engine. Unlike cylindrical axially symmetric objects, the rolling motion of a cone is such that while rolling on a flat surface, its center of gravity performs a circular motion, rather than a linear motion. Rolling objects are not necessarily axially-symmetrical. Two well known non-axially-symmetrical rollers are the Reuleaux triangle and the Meissner bodies. The oloid and the sphericon are members of a special family of developable rollers that develop their entire surface when rolling down a flat plane. Objects with corners, such as dice, roll by successive rotations about the edge or corner which is in contact with the surface. The construction of a specific surface allows even a perfect square wheel to roll with its centroid at constant height above a reference plane.
I've worked out how to derive the formulas for a solid cylinder and a solid sphere rolling down a hill.
E.g., for a cylinder:
Emech = KE + PE
mgh = 1/2 mv^2 + 1/2 Iw^2
gh = 1/2 v^2 + 1/2 (1/2r^2) v^2/r^2
gh = 3/4 v^2
v^2 = 4/3 gh
I then performed a derivative with respect to time and found a...
So I thought the stone would initially experience acceleration in the backward (leftward) direction then continually accelerate in the inward direction of the tire (i.e. upward then rightward then downward then leftward, etc.) as the tire moves forward. But the answer is immediately upward...
I am trying to understand the motion of the sphere in the image above, and I am a bit confused about the motion. How does the ball move down the cone? Will the rotation of the cone cause the ball to rotate with it, and which direction would the static friction be in? What does the path the ball...
About points 1. and 2., I assumed that the point of the sphere moving with maximum velocity is ##Q## and that the velocity at that point is ##v_Q= 2v##. In fact, at the highest point of a rotating sphere, the velocity is given by the sum of the velocities of translation and rotation. Since, in a...
Suppose a sphere is rolling on horizontal surface. The point of contact is the instantaneous center of rotation. It's velocity momentarily is zero. So in a time dt it'll stay where it is.
However during this time dt the point next to this contact point at its right side will move forward and...
Thank you guys for taking the time to read this - I'm decently struggling with first year and need some tips on how to properly conceptualize problems and learn what the right approach is on certain problems.
Have a wonderful day, again thank you for checking this post out!
Given that there is a cylinder rolling without slipping down an incline, the method I was taught to represent the KE of the cylinder was:
##KE_{total} = KE_{translational} + KE_{rotational}##
##KE_{total} = \frac {1} {2} mv_{cm}^2 + \frac1 2 I \omega^2## Where "cm" is the center of mass, and...
Hi I have come across something confusing in rolling motion. If an object moves with a positive V_cm meaning to the right its angular velocity will be clockwise or negative. The formula is V_cm=wR but for a positive V_cm you get a negative w as it moves clockwise if V_cm is to the right...
Here is the problem statement along with the figure.
Here, I take the right-ward and anti-clockwise directions to be positive.
After the ball collides with the wall, its angular velocity remains the same and its velocity changes direction while remaining the same in magnitude.
Using the...
I reasoned that at the coin's slowest velocity, the energy it has must just be enough for it to reach the highest potential configuration: when the point mass is directly above the centre of mass of the coin, and its GPE is ##mg(R+r)##. I used this to find the minimum velocity, but I can't think...
a=2/3*g*sin(25*(pi/180))=>a=2.8507 m/s^2
vf=vi+at=>vf=0+2.8507*1.50=>vf=4.2760 m/s
So the translational motion of the cylinder is 4.2760 m/s.
4.2760=R*w
w=134.04 rad/s
PE=mgh=>PE=215*9.8*.108=>PE=227.56 J
PE = KE at the end of the roll because of energy conservation.
227.56 =...
Say I have a magic way to exert lateral forces on a free-rolling ball on a plane, with no slipping. Say I apply a force for a given period from the South, the ball starts rolling to the North and attains a constant speed. Then I suddenly apply the same force for the same period but from the...
For part (c) of this problem,
My working is
However, the tricky part is to find theta. I tried to draw the situation so that I could find theta:
It appears that theta = 90 degrees. However, this does not seem to be correct. Does anybody please know how to correctly find theta in terms of...
Hi,
What is the formula or methodology for finding the Crr? There are many of those tests done on the internet, but none state the procedure of calculation. I'm trying to find the correlation between tire pressure and distance and want to use Crr as one of the key factors influencing it. Maybe...
Hi, I'm building a rolling mill for flattening out bits of steel and I'm trying to make sure it's not going to break.
I know that with a 1500w motor geared down to 60rpm (2pi rad/s) i end up with 239Nm of torque.
239Nm working at a radius of 0.0375m gives 6369N of force generated at the edge...
Suppose a cylinder is launched on a horizontal frictional surface such that it has initial translational velocity v and zero angular velocity .the kinetic friction would be applied between the contact points of the cylinder and the surface, opposite to the direction of the translational motion...
According to my current understanding
rolling friction
rolling friction is the static friction (parallel to the surface on which the object is moving) applied by the frictional surface (rough surface) on the contact point or contact area of the object whose v≠Rw(v is translational velocity and...
1)When a wheel is stuck in mud it rolls with slipping ,this means that at the point of contact it has a net velocity
As we can see from the image Kinetic Friction acts in the direction opposite to the resultant velocity ,this effectively reduces the tangential velocity at the surface and tries...
In pure rolling the of the sphere contact points of the sphere are at zero velocity,how is friction opposite to the motion of sphere being applied to these points?how the frictional force f is bieng applied to the sphere?
How will the friction work on a sphere which is purely rolling on a horizontal surface such that both the sphere and surface does not deform. The sphere at any time t will only have one point of contact, which would continuously changing as the sphere rolls. Will The friction be applied to the...
Consider an object, say a ball, rolling at a constant speed without slipping to the right on a horizontal surface. Let's consider the ideal case, so no deformation of ball or surface. For rolling without slipping to occur, there has to be friction (static friction as the point on the ball that...
There is no friction mentioned by the question so I assume the plane is frictionless but can the sphere roll without slipping if there is no friction?
This is my attempt:
Equation of translation motion of object A (assuming A moves upwards):
TA - WA sin θ = mA . aCOM (A)
TA = mA . aCOM (A) + WA...
A force is given to the center of the object so the object rolls to the right without slipping. I understand that to provide clockwise rotation the static force should be directed to the left.
But if the force F is located at the very top of the object, the static friction is directed to the...
I am posting this to generate a parallel discussion to this ongoing thread. It seems that some participants in that thread have doubts and confusion about rolling motion that might be better addressed separately from the homework problem in question. It is a simple test of one's understanding...
Hello everyone!
I'm watching this Walter Lewin lecture and am at 5:58 part of the video
I'm wondering how there's a frictional torque applied to the cylinder, my reasoning is that the object has forward velocity, and on a perfect cylinder, the slope of the incline touches the cylinder at a...
This is a problem that was posted here in 2003 and is now closed for replies. This question can be found at https://www.physicsforums.com/threads/friction-problem.662/
The answer in that old post didn't seem clear to me probably because it was highly summarized. There was no mention of static...
My question is about the contraint we need to use to solve this problem. The answer to the question use the following constraint:
$$(r+R)\theta = r\phi$$
Where $\theta$ is angle from the radius of the fixed cylinder to, say, the vertical axis. And $\phi$ is the angle that the rolling cylinder...
Question:
Galileo released a metal ball from rest so that it could roll down a smooth inclined
plane. The time t taken to roll a distance s was measured. He repeated the
experiment, each time recording the time taken to travel a different fraction of the
distance s.
Write an expression for the...
I don't understand why there is potential difference between point A and O. Is there any change in magnetic flux experienced by the ring? I think the magnetic field passing through the ring's cross sectional area is constant
Thanks
a) From impulse-momentum theorem I have: ##J=mv## so ##v=\frac{J}{m}## and since the ball doesn't slip ##v=\Omega b## so ##\Omega=\frac{J}{mb}## and ##\dot{\theta}=\frac{v}{a+b}=\frac{\Omega b}{a+b}##.
b) I considered the angular impulse: ##-J(a+b)=I_0 \Omega_0 \Rightarrow...
I figured the best way to do this is to focus on the second half of time. We can use the information there to find acceleration and that should make it fairly simple to find distance traveled in the first 5 seconds. Average speed in 5s-10s I found to be 40m/s.
My problem is that to find the...
Hello,
i have tried to calculate the acceleration (COM) of the cylinder (even though in the question they asked about the angular acceleration) and the answer is:
𝑎(𝑐𝑜𝑚)=𝐹(𝑟/𝑅−𝑐𝑜𝑠(𝑡ℎ𝑒𝑡𝑎))/(𝐼/𝑅2+𝑀)
and my answer is with minus (I/R^2 - M) . in their solution they wrote in the torque equation-->...
Hello everyone! I tried to solve this problem in a non-inertial system. Probably I should use the principle of conservation of mechanical energy in the following form
$$mgH = \frac{3mgR}{2} + \frac{mV^2}{2}.$$
So the only thing to do is to compute $V^2$. I tried to find this value using the...
I was looking for a way to calculate the friction arising from the axle and wheel of a standard lab cart. I came across this research paper: https://www.usna.edu/Users/physics/mungan/_files/documents/Publications/PhysEd4.pdf
That derived the following equation for the coefficient of rolling...
So, to obtain the motion equations I initially plotted the free-body diagram (see picture). Then I’ve tried to get equations, but I’m not sure, do I have done it rightl. I will be gratefull if someone could help me.
I am confused because according to my solution the disk is already rotating at constant angular velocity.
I have written the translational equilibrium on the horizontal and vertical component:
##N_1## and ##f_2## will have a positive horizontal contribution, while ##N_2## and ##f_1## will have a...
For this question i tried to reason with my self that C was the fastest and A was the second fastest. B would be the third fastest and D would be the least fastest since the ball has to go up. I looked up the answer and it says that C is the fastest , B and D are equal, and A is the slowest. How...
The acceleration and velocity of a body rolling down without slipping on a frictionless inclined plane are given by
$$
a=\dfrac{mg\sin \theta }{m+\dfrac{I}{r^{2}}}=\dfrac{g\sin \theta }{1+\dfrac{K^{2}}{r^{2}}} \cdots(1)
$$
$$...
I am stuck on problem presented about putting golf balls.
A stationary golf ball (mass=45g, dia=42mm, solid & homogeneous) is struck by a horizontal force (putter) and ignoring sliding immediately starts rolling on a level putting green. The ball eventually stops due to rolling resistance...
Hi,
I was reading this problem and I found a solution on Math Stackexchange which I don't quite understand.
Question: Calculate the expected value of the median of rolling a die three times.
Attempt: I read the following answer on math stack exchange here
"As already noted in a comment, the...
The problem is a classical one, basically to find the equations of motion of cylinder of radius a inside a fixed cylinder of radius b, the cylinder that rolls rotate about its own axis in such way that it does not skid/slip.
Now, the thing that is making myself confused is the constraint...
This looks like a physics question but it's not; it's an automotive question. Suppose you had a car at the top of a gently sloped hill, a 5% grade. You start it and put it in neutral or drive and it starts to roll down. You never place your foot on the brake or the accelerator and suppose the...
The following attempt gives the wrong answer, and I would like to know where it goes wrong.
Let ##\theta## be the angle of the ball with the vertical passing through the centre of the bowl, and ##\phi## be the angle the ball rolls through.
Let ##m## be the mass of the ball, ##r## be the radius...
So I tried the problem and it’s different from the solution. I’m confused on why my attempt didn’t work, is it because the wheel is undergoing general planar motion? I tried to just apply Newton’s 2nd law to find the acceleration of the centre and then use that to find angular acceleration. The...