Rolling Definition and 1000 Threads

Homework Statement A ball is rolled down a rough hill with coefficient of \mu<tan\theta. The hill has a height of h. The ball has moment of inertia of I, mass of m, and radius of r, which are all constant. What is the final velocity of the ball at the bottom of the hill? P.S. I made this...

Homework Statement a track is inclined in such way that the velocity of the metal ball is 60 cm/s at 25 degree below the horizontal. mathematically determine the total x displacement of the metal ball. weight of ball: 65grams height from floor to the end of the track: 76.15cm velocity of the...

Hi guys, I have an extremely simple conceptual question. According to my textbook (in a problem), "if you start a coin rolling on a table with care, you can make it roll in a circle... the coin leans inward, with its axis tilted." I ask: how is this possible? The center of mass of the coin...

Homework Statement A sphere of radius r and mass m rolls without slipping inside a hollow cylinder of radius R. z direction goes along axis of cylinder. Determine the Lagrangian with motion in the z direction included Homework Equations I let θ be the angle of the sphere rotation...

Hello, I'm running a couple of experiments in hot rolling and am in need of calculating the coefficient of friction during these experiments. All the equations I have found to calculate this during rolling all involve parameters like the roll bite angle which I am not sure how to calculate...

The question is: a spherical rock weighing 20 tons starts rolling down a steep incline from a height of 400 metres. Calculate the velocity when it reaches the ground level. What is the force exerted on the rock? I've tried to work this out but I just can't seem to grasp exactly what I'm...

Hi, I was thinking the other day of two soup cans of different types(one cream one consomee) rolling down a slope. I was thinking that the non-cream one (consomee) will always roll longer, but was surprised to find out that past a certain angle the cream soup was going longer. By longer I...

In the diagram below, a cart is released from rest at a distance x1 from the first of two photogates. The cart then rolls down the ramp through both photogates. The distance between the photogates is x2. For this problem, you may assume that the cart is frictionless and the acceleration of the...

Hello, I am trying to derive the equations of motion for a system that is essentially an inverted pendulum on a wheel. The pendulum is connected to the wheel by a motor. I have a motor torque M and a disturbance torque D. The radius of the wheel is r. My generalized coordinates are the...

Homework Statement A billiards ball (mass m) is hit by a billiard stick on the center of the ball (from the side) with a collision impulse mv0 so that the cues line of travel goes straight through the center of mass of the billiards ball, which in the collision-approximation gives a speed v0...

Well, I've recently been introduced to the wonderful world of angular momentum and precession motion, and a question popped into mind. Why, exactly, does a wheel rolling across the ground, not topple over even if tipped to one side? I've tried approaching the problem by looking at the angular...

newbie question, say I'm rolling a ball down a smooth , differentiable, and frictionless 1-Dimensional hill V(x) from a point x_i find the location x(t) and the velocity dx/dt(t) of this ball at some arbitrary time t. what would be the general approach towards such a problem? note that for...

Hi, When a circular section object (cylinder, sphere of radius r) rolls down an inclined plane (at angle theta) it experiences both linear and angular acceleration due to gravity. I have read multiple times that: mg sin(theta) - friction = m a where friction = Torque/r From there on...

Why is the normal reaction to a rolling object shown to the side of the CM? Forces must be equal and opposite Is there a real problem if you assume it through the C?

Hello ! Is there an expression for the friction force exerted on a solid sphere rolling (or rolling and slipping) on a rough solid inclined plane ? I have searched a lot but couldn't find anything, most studies are related to caoutchouc spheres or plane that will deform anbd cause viscoplastic...

Homework Statement A Block slides down a frictionless ramp and a sphere rolls without sliding down a ramp of the same angle. the block and sphere have the same mass, start at rest from point A and descend through point B a) Consider the sphere rolling down the incline without sliding. If...

Homework Statement A solid sphere of uniform density (weight = 3.2 lbs starts from rest and rolls down a ramp (H = 1.57 m, q = 18.3°.) Find the speed of the sphere's CM when it reaches the bottom of the ramp. haha sorry bout that... Homework Equations see below The Attempt at a...

Hi. I am doing an experiment on golf balls. I know that the dimples are supposed to reduce the resistance when traveling through the air. I am testing the effects that dimples have on rolling resistance when on the ground. I am using 3 golf balls of the same type/brand. One, I am keeping it...

Homework Statement A sphere of radius r_0 = 24.0 cm and mass m = 1.20{\rm{ kg}} starts from rest and rolls without slipping down a 37.0^\circ incline that is 15.0 m long. Calculate its translational speed when it reaches the bottom. Homework Equations ke=1/2mv^2 pe=mgh The Attempt...

Homework Statement 125N of force are required to compress a spring by 1.04m. The cart rolls across the table at a constant speed. It then rolls up an inclined board and comes to rest. How high above the table is the cart when it stops? Homework Equations The Attempt at a Solution

I came across an interesting little problem doing some work that I though I'd share. Typically, we think of three types of resistance for a wheel: Static Friction Kinetic Friction Rolling Resistance I'm modeling the wheel of an airplane for a flight simulator. When the airplane is sitting...

A cylinder rolls up an inclined plane, reaches some height, and then rolls down. The directions of frictional force acting on the cylinder while descending will be up the inclined. But what will be the direction of frictional force when the cylinder is ascending?? UP or DOWN Well, I think...

Hi everyone I work for a very small company, which produces steel products. Predominately from one particular hot rolled steel profile. (1040 grade) We currently subcontract our hot rolling to small chinese operators :( I know... At this stage our volumes are not large enough to warrant...

Homework Statement A thin cylindrical shell and a solid cylinder have the same mass and radius. The two are released side by side and roll down, without slipping, from the top of an inclined plane that is 1 m above the ground. The acceleration of gravity is 9.8 m/s2. Find the final linear...

Homework Statement Assume that there is no slipping of the surfaces in contact during the rolling motion. A motorcycle accelerates uniformly from rest and reaches a linear speed of 22.0 m/s in a time of 9s. The radius of each tire is 0.280 meters. What is the magnitude of the angular...

I have a very simple conceptual physics problem that I am looking to solve, and unfortunately I've been out of school a little too long to solve: Suppose you have a hill, and at the bottom of the hill it levels off and keeps going on. You take two marbles of different masses and roll them...

Homework Statement A uniform solid cylinder of mass `m' and radius `a' rolls on the rough outer surface of a fixed horizontal cylinder of radius `b'. Let `theta' be the angle between the plane containing the cylinder axes and the upward vertical (generalized coord.) Deduce that the cylinder...

Homework Statement A 181 g ball is released from rest H=5.19 m above the bottom of the track shown in Figure. It rolls down a straight 21° segment, then back up a parabolic segment whose shape is given by y=x2/4, where x and y are in m. How high will the ball go on the right before reversing...

Homework Statement Hi again ,, my second one is easy: A tire 0.5 m in radius rotates at a constant rate of 200 rev/min. Find the speed and acceleration of a small stone stuck on the surface of the tire (on its outer edge). Homework Equations The Attempt at a Solution the Speed...

If we have an inclined plane at angle \alpha and a sphere on that plane it will have angular acceleration due to the friction force. If F_{lim}<mg\sin \alpha , where F_{lim} is the limiting friction will the sphere also slide along the plane?

FORCES On a bridge A bridge, constructed of 11 beams of equal length L and negligible mass, supports an object of mass M as shown. (Intro 1 figure) Real bridges of this sort have steel rockers at the ends (check one out sometime), these assure that the support forces on the bridge are...

Homework Statement A uniform cylinder of mass M and radius R has a string wrapped around it. The string is held fixed, and the cylinder falls vertically. (a) Show that the acceleration of the cylinder is downward with a magnitude a=2g/3. (b) Find the tension in the string. Homework...

Homework Statement A point mass m is attached to the rim of an otherwise uniform solid disk of mass M and radius R (in the diagram mass m is in contact with the ground). The disk is rolled slightly away from its equilibrium position and released. It rolls back and forth without slipping...

Homework Statement If you put a ball somewhere on a slope and it rolls down, how far will it go when the ramp is at some hight over the ground and the output angle is something.Do not take in account friction or air resistance. Homework Equations The Attempt at a Solution When u put the ball...

A uniform solid sphere of radius R and massM rolls without slipping on a horizontal plane. The centre of mass of the sphere moves initially with velocity ~v directed perpendicularly to a fixed block of height h < R. The sphere hits the block and the collision is such that the point P on the...

Homework Statement Hi there - I'm working through a bit of mechanics revision and have been looking at some of my uni past exam papers from a good few years back when the syllabus was different, so I'm not familiar with a lot of the material covered - it's not strictly relevant to my current...

Homework Statement In the given arrangement a sphere of mass "m" rolling on a rough surface strikes a rough inclined plane. Find the velocity of centre of mas and the angular velocity of sphere if just after collision, it starts ascending up the incline plane and performs rolling...

Energy "lost" in rolling, sliding and torsion Hey everybody, I have a question concerning three states and the state of energy in them. 1. Rolling 2. Sliding 3. Torsion For example: If I have a steel cylinder with diameter d on an axis (no friction in the axis) rolling horizontally over a...

Homework Statement Minimum Angular Speed to start SLIPPING BEFORE ROLLING WITHOUT SLIPPING. Homework Equations A cylinder of mass M with radius r is given an angular speed of an w about an axis, parallel to its length , which passes through its centre. The cylinder is gently lowered onto...

"Rolling" Chalkboards I've been trying to find a supplier of rolling chalkboards (on a spool). When you google the term you are given nothing but "reversable chalkboards" (on a stand, flipping between sides). This would be for personal use, I'm not a lecturer or anything. I'd just like one...

Hi there currently I am stuck on a question, A car with a mass of 1.2 tonnes, rolls down a hill which is 600m long and is inclined at an angle of 9 degrees to the horizontal. Ignoring the effects of air resistance and friction and assuming the car to start from rest at the top of the hill...

1. A solid sphere has a radius of 0.200 m and a mass of 150 kg. How much work is required to get the sphere rolling with an angular speed of 50.0 rad/s on a horizontal surface? Assume the sphere starts from rest and rolls without slipping 2. The attempt at a solution I found V first. V= rw =...

Homework Statement Roll 7 dice. What is the probability that the sum of the numbers is 14? Homework Equations Possibly a probability generating function because the problem comes from the chapter that deals with it but I can't think of which one (if any actually apply). The...

A uniform disk of mass m and radius R rolls without slipping down a ramp inclined at angle q to the horizontal. Using the angle f through which it turns as a generalised coordinate, write the lagrangian, and then the Hamiltonian. Write out and solve Hamilton’s equations of motion. Ok, so...

Homework Statement Describe how you could use the procedure from this experiment to measure the coefficient of rolling friction between the tires of a car and the road surface for different pressures of air in the tires? Procedure = 1. Slide a mass along the surface of a lab desk and...

Homework Statement A constant horizontal force app of magnitude 15 N is applied to a wheel of mass 8.9 kg and radius 0.39 m. The wheel rolls smoothly on the horizontal surface, and the acceleration of its center of mass has magnitude 0.76 m/s2. (a) What is the magnitude of the frictional force...

Homework Statement Five dice are rolled. You win a dollar for each number other than a five that is rolled, but you don't win extra for duplicate numbers; for example if [3,5,3,2,1] is the result, then you win three dollars. What should you pay to play this game (what is expected value)...

Homework Statement A small ball of radius 1.9 cm rolls without slipping down into a loop-the-loop of radius 3.7 m. The ball has mass of 353 gm. How high above the top of the loop must it be released in order that the ball just makes it around the loop, and what is the total kinetic energy...

Homework Statement A wheel with mass m, inner radius r and outer radius R is placed on a slope. The slope has angle θ related to horizontal. When the wheel is affected by a constant, known torque Tau in the centre of mass, the wheel begins rolling uphill...

a steel ball, starting from rest rolls down one slope and up another. it takes 2.5s to reach the bottom of the first slope, at which point its speed is 5.0 m/s. if the magnitutde of the acceleration on the second slope is exactly one-half that on the first slope, how long will it take for the...