Rolling Definition and 1000 Threads

Ok so please bear with me here and what is almost certainly a really stupid question, partly because I don't quite know how to ask it. When you have a wheel such as one attached to a car, a torque is applied to it from the engine. It's my understanding that the wheel would slide over the road...

I know the ans comes out to be mgsintheeta/3 by using f=ma and the torque eqn but my question is as stated in the question the cylinder is in pure rolling hence friction should only try to oppose mgsintheeta so that the accelration does not change hence v remains equal to rw so why is the ans...

Hi, I've been following the derivation of wolfram mathworld for this problem and I'm running into some trouble regarding the summation indices. Currently I am at the step where we have found that (it's pretty much just binomial expansion and taylor series to get to this point) $$ f(x) =...

Figure: a) The mechanical energy of the sphere is conserved because the weight is the only force which does work. My problem with this question is mostly because the original picture (which I tried to recreate here) is kind of ambiguous, as in I don't know if H already accounts for the radius...

Problem Statement: Let there be a ring of mass m and radius r. Let 3 masses be attached to the ring and named as O,P and Q. Mass of O and Q is 2m and mass of p is M. The angle between 2 masses is 15 degrees as shown in the figure. Find the maximum velocity the ring must roll so that it doesn't...

So looking at the solution, FBD for A makes sense: Normal points inwards, gravity and friction oppose each other, with friction pointing up. B confuses me: the solution says there is only Normal and gravity pointing downwards, but if "the sphere rolls without slipping during the entire motion"...

I've been teaching myself Probability Mathematics, but I'm still struggling. Please help me understand with an example. Say I roll five six-sided dice all at once, with die faces numbered 1 through 6. I want to determine the probability of AT LEAST three 6s occurring. First, is this the best...

Forces in the x direction: static friction left=Tcostheta to the right Forces in the y direction: W= Normal force + Tsintheta Net torque: rTcostheta-RFs=0 Fs=Tcostheta, rTcostheta-R(Tcostheta)=0 rTcostheta=RTcostheta r=R Please help

Hi. My question is regarding toy car A. If the car moves to the left, is the constant acceleration of ##2.40 \frac {cm} {s^2}## to the left or to the right?

Hey! :o Tim rolls $20$ times a fair dice. Calculate the probability to get a "$3$" exactly $8$ times. The probability to get at least $k$ times a "$5$" is equal to $10,18\%$ Calculate $k$. Explain the relation to the term $\displaystyle{\sum_{i=0}^2B\left (10;\frac{5}{6};i\right )}$...

A marble rolls down an inclined plane with an angle of elevation of 5 degrees, roughly 4.9sin(5)m/s/s, and at normal pressure temperature NPT what would I need to add to S=1/2 at^2 to include the air resistance considering the marble is a sphere with a radius of 0.85cm and mass of 20g. The whole...

So the kinematics of the contact point of a disc rolling without slip in a Cartesian plane if fairly straightforward. The velocity for the contact point is just v = ω r ev where r is the wheel radius and ev the current direction vector of the wheel. However, say that you grab the plate and...

Homework Statement A cylinder with a mass of M and radius R is attached to a spring with a constant of k. The attachment always stays the same as described in the picture. The cylinder is moved to the right and the released, and it rolls without slipping (pure rolling). What will be the...

Homework Statement A solid cylinder rolls down an inclined plane because of stiction. How does angular velocity change over time? Given: ##m,R,g,\alpha,\mu## where ##\mu## is the friction coefficient Homework Equations [/B] ##J_{cm} = 1/2 m*r^2## moment of inertia m = mass of the cylinder...

Homework Statement A thin plank of mass M is placed centrally across two solid cylindrical rollers each of mass m, and the system is allowed to move freely from rest without slip down a slope of angle θ as shown in the figure below. (a) Derive expressions for the initial accelerations of the...

Suppose that we have a some rotating object (lets say a wheel with radius R). Let's observe this problem from some reference frame in which center of mass translates with some velocity v and rotates with angular velocity ω. I know that condition for rolling without slipping is v=ωR (point at...

Homework Statement Please see the attached file. Homework Equations Ei = Ef The Attempt at a Solution I don't have an answer key provided, but I'd really like to verify that I'm right (or if I'm wrong, why). I think ti'd be (c) because assuming that due to inertia, B will continue going...

Homework Statement A rectangular board laying on the ground of mass ##M## is pulled with a force ##F## to the right, while a cylinder of mass ##m##, radius ##R## rolls without slipping on the board. Assume there is no friction between the board and the floor. Which way does the cylinder roll...

Homework Statement A solid sphere, hollow sphere, disk and ring are released simultaneously from top of a incline. Friction is sufficient to prevent slipping of hollow sphere- what will reach the bottom first? Homework Equations a in pure rolling down an incline=gsinθ/(1 + I/mR^2) The Attempt...

Homework Statement I want to prompt the user to input how many times they want to roll a die, then generate a random number between 1 and 6. I then need to print what their number is and if it is even or odd. The code I posted below is what I came up with for a single die roll that allows...

Homework Statement A rigid cylinder of radius ##R## and mass ##\mu## has a moment of inertia ##I## around an axis going through the center of mass and parallel to the central axis of the cylinder. The cylinder is homogeneous along its central axis, but not in the radial and angular directions...

I was wondering that if rolling resistance is basically caused by slight deformation of a body, we must have formulas in place to relate it to the physical and material properties of a body. But when I went ravaging for it in library or internet, everything was experimental. I wished to know...

Homework Statement If two balls, being identical in volume, but different in density (one ball is made of iron, the other of aluminum) roll down from an inclined plane, which will reach the bottom first and which will cover a larger distance after having reached the bottom? IMPORTANT NOTE...

I have conducted an experiment that measures the velocity of an object that is moving on a flat surface. The object rolls on four fixed caster wheels. The wheels are made of some kind of rigid material. Maybe nylon, maybe hard rubber. The total mass of the object, including the wheels, is...

Homework Statement A metallic spherical shell of mass M and radius R is fully filled with water of mass M is set into pure pure rolling motion on a smooth horizonal surface (w clockwise, v to the right). Now water is freezed suddenly, and the ice sticks with the shell. What is- a) moment of...

Homework Statement A disk is undergoing pure rolling motion with speed v. The radius of the disk being R and mass M. Then the angular momentum of the disk about the 1)bottom most and 2)top most point Homework Equations 1) L(orbital) = m*v*r where v is the velocity of cm which is...

1. The problem A ball moves without sliding on a horizontal surface. It ascends a curved track upto height h and returns. Value of h is h1 for sufficient rough curved track to avoid sliding and is h2 for smooth curved track, then how are h1 and h2 related (greater, lesser, equal or multiplied by...

Homework Statement A long plank of mass M rests upon a smooth horizontal surface. A thin circular ring (m, R) slips (without rotation) upon the plank with initial velocity v(i). The coefficient of friction between the wheel and the plank is C. at time t, the ring stops slipping and pure rolling...

Homework Statement A solid circular disk (m,R) translates with v1 and rotates with angular velocity w1=2v1/R, at t=0. Because of friction, pure rolling starts at time t. the coefficient of friction is C. Find velocity of center of disk at time t Homework Equations 1) for pure rolling v=Rw 2)...

Hello, This is an investigation I have been studying recently, can someone help with the following... 1. Homework Statement Method: 1. Place a toy car at the top of a ramp. 2. Let it go. 3. Measure the distance it travels from the bottom of the ramp. 4. Add a 100 g mass to the car and...

Homework Statement which ball reaches at the end of the board first, which ball reaches ground first, which ball would be fastest when reached ground and at the end of the board? heights are same and balls are identical Homework EquationsThe Attempt at a Solution i think since ball rolls...

Homework Statement If we have a hollow ball completely filled with water which is rolling without slipping on a horizontal ground. If the water freezes which of the parameter will remain unchanged- angular speed, angular momentum, linear momentum, kinetic energy, total energy Homework...

Homework Statement Find the acceleration of a uniform solid sphere (of mass ##m## and radius ##R##) rolling without slipping down an incline at angle ##\alpha## using the Lagrangian method. Homework Equations Euler-Lagrange equation which says, $$\frac{\partial\mathcal{L}}{\partial...

Homework Statement A 1450-kg car is towing a trailer of mass 454-kg. The force of air resistance on both vehicles is 7471N[backward]. If the acceleration of both vehicles is 0.225m/s^2[forward], what is the force of static friction on the wheels from the ground? Homework Equations Fnet = ma...

in case of rolling without slipping of a solid sphere having uniform mass density the condition is Vcm (velocity of center of mass ) = Rω or [a][/cm] = Rα ,which comes from the fact that if an object that rolls without slipping the geometric center of the body travels 1 circumference along...

Homework Statement A loaded railroad car is rolling at a constant velocity when it couples with a spring and dashpot bumber system. After the coupling, the motion of the car is defined by the relation ##x = 60e^{-4.8t} sin16t##, where x and t are expressed in millimeters and seconds...

Homework Statement Given a cylinder is rolling purely and a man with mass m is attatched to a point in the circumference of the cylinder. As the man approaches the lowest point he jumps vertically up. Will the velocity of the cylinder increase, decrease or remain same after the man is detached...

Homework Statement Estimate the rolling resistance force for a 75gram vehicle with axle friction coefficient of 0.2 if the wheel is 40mm diameter and the axle 2mm diameter. I am having trouble with applying the axle friction coefficient. I could not find a similar problem online. Basically...

Homework Statement Homework Equations inertia equations The Attempt at a Solution I think the answer for this is B) or D) but I am not sure what the sentence "a special solid cylinder in which the density is proportional to the radius" means... The solid sphere has little inertia because...

Homework Statement A perfectly solid marble of radius R rolls without slipping at the bottom of a spherical bowl of a radius 6R. The marble rolls back and forth in the vertical plane executing simple harmonic motion close to the lowest point. How long does it take the marble to go down one side...

A standard six–sided dice is rolled repeatedly and a running total is kept of all the numbers rolled. Which of $2, 6, 1006$ is more likely to be one of these totals? Prove your answer.

I am comparing three brands of tires to see which one provides the lowest rolling resistance and thus give the best efficiency at low speeds. I have the information of the tires such as footprint, weight (of the tire and load), speed. How would i go about doing this ? am really stumped thanks

I am making a physics simulator and this problem is tricky. You have two freely moving objects with known masses and velocities in a frictionless environment. The first object is a ball and the second is a pipe. They are moving toward each other. I need to know what formulas are used to simulate...

Check Attached file for questionI am not able to get the equations for motion. Except that when cylinder loses contact, the normal force is zero.Please answer this fast. Need it for a test tomorrow. Thanks a lot!

HOMEWORK POSTED IN WRONG FORUM. WE AWAIT SOME EFFORT ON THE PART OF OP BEFORE CONTINUING. A cylinder C1 of mass M1 and radius R1 is placed on top of another cylinder C2 of mass M2 and radius R2. C2 is kept rigidly fixed (so that it can neither translate nor rotate). C1 starts rolling without...

Homework Statement A ball with moment of intertia bmr^2 rolls without slipping down a plane inclined at angle O. What is it’s linear acceleration? Homework Equations Fnet= ma T = F x r T = IO’’ a = rO’’ The Attempt at a Solution Fnet = mgcos(O) - FfT = FfrT = IO’’ Ffr = bmr^2O’’ Ff =...

I am doing some calculations to optimize the power to weight ratio and gearing of a RWD car. I have torque charts and can calculate the force put to the track by each wheel and the static frictional force by the track on each wheel. I am trying to determine what the minimum speed is for the...

Let's imagine a situation where we have a wheel of mass ##M## and radius ##R## on a frictionless surface, and we apply a force ##\vec{F}## as shown in the diagram. The force will produce both linear acceleration of centre of mass ##a## and angular acceleration ##\alpha##. The wheel starts to...

Homework Statement A solid sphere of mass m=2.5 kg is rolling at v=5.3 m/s. Calculate the transitional kinetic energy, rotational kinetic energy, and the ratio of the two (Rotational/ Transitional). Homework Equations [/B] Inertia of solid sphere = 2/5 mR^2 (where R is the radius and m is the...

Mentor note: Moved to homework section A conical wheel is rolling (without slipping) around a fixed axis OZ as shown in the figure. The velocity of point C is vc = at. The direction of the velocity of C is shown by a cross i.e. along negative x-axis. We have to find the angular velocity...