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.
Homework Statement
A billiard ball (of mass m and radius a) is struck by a cue and moves off with initial speed u, sliding (without rotation) along the table top. After what time will the ball roll rather than skid, if the frictional force between the ball and the table has magnitude qmg...
A bicycle racer is going downhill at 11.0m/s when, to his horror, one of his 2.25kg wheels comes off when he is 75.0m above the foot of the hill. We can model the wheel as a thin-walled cylinder 85.0cm in diameter and neglect the small mass of the spokes.
I need to get the velocity at the...
Ok,
First of all, for the formulas torque = r X F
If the object is being rotated around an axis parallel to the axis going throught the center of mass, what is the "r" in this case? is it the distance from the axis of rotation to the center of mass? And in what direction would the force...
Homework Statement
A rolling ball traveling horizontally with a certain initial translational velocity comes to a hill with a defined height. Upon reaching the top, it flies off of a cliff and falls to the ground and ends up at the same relative height that it began at. If the final diagonal...
Homework Statement
A hollow spherical shell is rolling without slipping or sliding down a board that is tilted at an angle of 35.0° with respect to the horizontal. What is its acceleration?
Homework Equations
I=2/3mr^2
if an object rolls without slipping or sliding:
v = rw...
Homework Statement
a roof makes an angle of 30deg with the horizontal. A ball rools off the edge at a speed of 5.0 m/s. The distance to the ground is 7meters. How long is the ball in the air?
Homework Equations
0=Vot-1/2gt^2+y
t=(vo+/- sqrt(vo^2-(4*gy)))/g
The Attempt at a Solution...
Pebble in a rolling tire -- finding velocity and acceleration
Homework Statement
ou are to find the coordinates of a pebble stuck in the tread of a rolling tire that is rotating counterclockwise (i.e., in the positive sense) with angular velocity w. The tire rolls without slipping on the...
HI there, I'm a practicioner of Parkour, which is a discipline that involves training to allow yourself to pass any obstacles simply using your body.
One of the movements which we use is a roll, designed to aid landing from height.
As I understand it, the basic idea is that the roll...
Homework Statement
You are to find the coordinates of a pebble stuck in the tread of a rolling tire that is rotating counterclockwise (i.e., in the positive sense) with angular velocity omega. The tire rolls without slipping on the ground (which is at y = 0 ). The outer radius of the tire is...
Homework Statement
A ball of mass 2.80 kg and radius 0.148 m is released from rest on a plane inclined at an angle θ = 38.0° with respect to the horizontal. How fast is the ball moving (in m/s) after it has rolled a distance d=1.55 m? Assume that the ball rolls without slipping, and that its...
Homework Statement
A ball of mass 2.30 kg and radius 0.142 m is released from rest on a plane inclined at an angle q = 42.0° with respect to the horizontal. How fast is the ball moving (in m/s) after it has rolled a distance d=1.35 m? Assume that the ball rolls without slipping, and that its...
HELP - Energy of a rolling sphere (no radius??)
Homework Statement
A solid sphere of mass 0.602 kg rolls without slipping along a horizontal surface with a translational speed of 5.18 m/s. It comes to an incline that makes an angle of 34degrees with the horizontal surface. Neglecting energy...
A 500g, 8.0-cm-diameter can rolls across the floor at 1.0 m/s. What's the can's kinetic energy.
I solved this using:
K = \frac{1}{2}*I*(\frac{v}{r})^{2}
and for some reason I get 1/3 the answer. So I multiplied it by 3 at the end. Is there something wrong with the formula I'm using...
A 1kg ball rolls along a circular track that is banked at 20 degrees. The normal force on the ball is 10.43N, tilted inward. The radius of the track is 10m.
a. What is the net force on the ball (include direction)?
b. How fast is the ball going for it to complete the turn?
possible...
Homework Statement
The graph shows the speed as a function of time for a minivan, coasting on neutral along a straight, level road, loaded with windsurfing equipment and towing a boat.The total mass is 2450kg (weight = 5402lbs). Find the size of the force due to wind and rolling friction when...
Homework Statement
A uniform hoop of mass m and radius r rolls without slipping on a fixed cylinder of radius R. The only external force is that of gravity. If the smaller cylinder starts rolling from rest on top of the bigger cylinder , use the method of lagrange multipliers to find the point...
Homework Statement
A 12g CD with a radius of 7.0 cm rotates with an angular speed of 35 rad/s.
What is its kinetic energy?
Homework Equations
The Attempt at a Solution
I used K=(1/2)mv^2(1+I/mr^2)
v=\omegar=(35rad/s)(0.07m)=2.45m/s
K=(1/2)(0.012kg)(2.45m/s)^2(1)=0.36
And...
Word for word:
A50,000kg locomotive is traveling at 10 m/s when its engine and breaks fail. How far will the locomotive roll before it comes to a stop?
Rolling friction for rubber on concrete is 0.02 (by the book)
a= fnet/m = (umg)/m so mass cancels out leaving a = ug = .02(-9.8) =...
All the drums weigh the same...one has greater surface area , one has center of mass in the middle...and one has center of mass at an end.
Which will get to the ground first?
When I think I am starting to understanding mechanics, I spot questions like these... If I am having problem w/...
Homework Statement
Two bicycle tires are set rolling with the same initial speed of 3.00 along a long, straight road, and the distance each travels before its speed is reduced by half is measured. One tire is inflated to a pressure of 40 and goes a distance of 17.2 ; the other is at 105 and...
I'm an Applied Physics major (considering switching to plain, vanilla Physics), and I've been working on this problem forever. It's not homework; only something I've been trying to work out, in bits and pieces, over the past few weeks in my spare time. It's for a game called D&D, which I'm sure...
Homework Statement
A 684 kg automobile is moving at 13.2 m/s at a height of 5.0 m above the bottom of a hill when it runs out of gasoline. The car coasts down the hill and then continues coasting up the other side until it comes to rest. Ignoring frictional forces and air resistance, what is...
[SOLVED] Rolling Friction
Homework Statement
Rolling Friction. Two bicycle tires are set rolling with the same initial speed of 3.30 m/s along a long, straight road, and the distance each travels before its speed is reduced by half is measured. One tire is inflated to a pressure of 40 psi...
2-D kinematics[solved]
Homework Statement
A ball rolls horizontally off the edge of a tabletop that is 1.90 m high. It strikes the floor at a point 1.57 m horizontally away from the table edge. (Neglect air resistance.)
(a) How long was the ball in the air?
(b) What was its speed at...
Homework Statement
So I need to get a rough calculation:
At what angle does drops of water start rolling down a plane of glalss.
This is for my project where we are using a solar still to purify water. I just need ot get a rough calculation so I know at what angle to tilt the plane of glass...
Homework Statement
Imagine a cannon that is free to roll on wheels. Initially, both the cannon and cannonball are at rest. When the cannonball is fired, though, the momentum transferred to the cannonball comes at the expense of the cannon, so the cannonball and cannon end up with momenta...
Homework Statement
Hello, new here. I'm doing homework for my Honors Physics class, and I have a kinematics problem that seems simple enough, but I just can't get it. Help, please?
A ball is rolling on a table 1.225 m high at 6 m/s. After it rolls off, how long does it take to hit the...
Hi.
Ok, I've given this question already soooooo much time and I simply cannot solve it.
Homework Statement
There's a circular surface that's holding still (like a bowl), with radius R, and a ball, with radius r, on it.
The ball is rolling without sliding.
The mass of the ball and it's...
Hi everyone,
I'm kinda new and I'm trying to understand some kinematic principles which I can't really figure out...
Without using intuition, what is the proof behind in explaining that the velocity of a rolling ball down a straight ramp increases and the velocity decreases when the...
No idea where to start with this one, any help is much appreciated...
"A metal plate needs to be reduced to a thickness of 4 cm by involving a rolling mill. After rolling, the elastic properties of the material cause the plate to regain some thickness. Calculate the needed separation between...
when we say that in pure rolling the speed of the point of contact is 0 do we really mean it's just absolutely 0 or is it negligible.this may seem strange...
but if it's 0 then why does that point ever move.if it ever moves then it's speed is no more 0 ...
Homework Statement
A solid sphere of radius 20cm is positioned at the top of an incline that makes 22 degrees angle with the horizontal. This initial position of the sphere is a vertical distance 1.8m above its position when at the bottom of the incline. Moment of inertia of a sphere with...
Rolling Friction?
Can someone explain to me why the frictional force is in the same direction as the acceleration of the center of mass of a rolling object?
Homework Statement
A bug of mass m is stuck to a point on the rim of a rolling wheel (of radius r)... which traces out a path called a cycloid. The position vector of the point (bug) is given by:
r(theta) = r(theta - sin(theta))i + r(1 - cos(theta))j
For a wheel rolling with constant...
Homework Statement
A uniform solid sphere (moment of inertia = 2/5 mr^2) of mass 1.5kg and radius r = 0.473m, is placed on the inside surface of a hemispherical bowl of radius R = 2.77m. The sphere is released from rest at an angle of 66.9 degrees from the vertical and rolls without...
Homework Statement
A ring of mass 2.83 kg, inner radius 5.30 cm, and outer radius 6.95 cm rolls (without slipping) up an inclined plane that makes an angle of θ=37.4°, as shown in the figure below.
http://capa.physics.mcmaster.ca/figures/sb/Graph11/sb-pic1106.png
At the moment the ring...
Hello,
I need some help in resolving a dispute. Recently, a friend of mine told me that the probability of rolling a 6 on the second roll of a die after not rolling a 6 is not 1/6. He believes it is not 1/6 but rather the probability of rolling 6 after not rolling a 6 increases with each...
The title really says it all.
Lets say i have a ramp, 1 meter long, that is at a 32 degree tilt. I place a ball on the top of the ramp and let if role down the ramp (no friction). 1. How long should it take for the ball to get near the bottem and 2. Since the ball is falling what is the ball's...
Homework Statement
Alright for this thing, we had to pull a cart up a inclined plane and time how long it took to get to the bottom.
Distance from ground to top of inclined plane is - 0.125m
Length of Board is - 1.21m
Mass of cart - 1.09kg
Force to pull cart up - 1.4N
Time it took for...
A ball rolls across a table and stops due to rolling friction. It has a mass of m and travels a distance of s in the time t.
What is the ball's initial speed?
The same ball rolls until it hits a wall. It has a mass m, and traveled a total distance of s (to the wall) in the time t.
What...
A solid sphere rolls without slipping down a ramp that is at an angle of 32 above horizontal. The magnitude of the acceleration of the center of mass of the sphere as it rolls down the ramp is?
sum of torques = I(alpha)
rmgsin32 = (2/5)mr^2(a_tan/r)
the radii drop out as one would...
Homework Statement
A wheel of radius R rolls along the ground with velocity V.
A pebble is carefully released on top of the wheel so that it is instantaneously at rest on the wheel.
(a) Show that the pebble will immediately fly off the wheel if V> sqrt(Rg)
(b) Show that in the case where V<...
Hello,
I'm a student currently nearing the end of high school, so my knowledge of physics (or even general math for that matter) are somewhat . . . lacking. That said, I'm currently attempting to figure out the various simple principles that apply to rolling a pair of dice across a table...
Homework Statement
A hoop is launched so that it slides with backspin across the floor. Due to friction on the floor, the hoop eventually reverses direction. A little after that, it stops slipping and rolls back to the point where it was launched. If the initial speed of the hoop was v and...
if a rear wheel driven car is accelerated
i think...
1. on rear wheels friction is forward
2 on front wheels it is backward
my questions-
1.wats d direction of rolling friction on the car as a whole?(is dis question correct?)
2.which wheel will have greater magnitude of friction??
I need help with this...
A hollow, thin walled cylinder and a solid sphere start from rest and roll without slipping down an inclined plane of length 3 m. The cylinder arrives at the bottom of the plane 2.4 seconds after the sphere. Determine th angle between the inclined plane and horizontal.
Suppose a solid disk of radius R is given an angular speed about an axis through its center and then lowered to a horizontal surface and released, the coefficient of friction between disk and surface is u. What is the distance traveled before pure rolling occurs?
Conservation of Momentum...
Homework Statement
I throw a ball rolling and moving through the a flat surface. I may say that friction is slowing down translation motion, but increasing rotational motion, so when the ball stops moving, why is it not rolling? That's confusing me a bit. What can you say?
Help! Plane motions rolling wheel
Hi there, I am not having any luck with this question at all and am hoping that there is someone out there that can help me out... here goes:
The below cyclinder rolls to the right at 10 in/sec. Determine the angular velocity of BC and CD
I am actually...