Rotational dynamics Definition and 274 Threads

So I first wrote the moment of inertia of the cylinder, since it says that it is thin-walled, I think that its moment of inertia is ##I=\eta mR^2##. After that I wrote the sum of torques, I think that there are three forces that cause torque, the two forces of friction, the one caused by the...

I already solved the first part, but according the my book, the answer isn't quite correct. This is what I did. Finally, I ended up with ##a=\frac{F(r-R\cos\alpha)}{Rm(\gamma+1)}##. But according to my book, the answer is ##a=\frac{F(\cos\alpha-\frac{r}{R})}{m(1+\gamma)}##, what am I doing...

I am doing a project, but am struggling to find relationships of proportionality or formulae between my dependent variables (angular velocity, displacement, acceleration of the disc and kinetic energy of the system) and my independent variables (falling masses and then the number of winds) or...

Homework Statement I have attatched both the problems. The figure is essentially the same. Homework Equations 1. Energy conservation 2.mgcosx - N = mv^2/r , where N is zero in limiting case. The Attempt at a Solution I solved the whole question and got the answer given in irodov(0.33...

Homework Statement This problem was originally posted on Physics Problems Q&A: http://physics.qandaexchange.com/?qa=616/friction-between-two-disks Homework Equations Second Newton's law for rotation: $$\tau = I \alpha = RF$$ The Attempt at a Solution I tried to solve this problem as...

Homework Statement You buy a bottle of water in the store and place it on the conveyor belt with the longitudinal axis perpendicular to the direction of movement of the belt. Initially, both the belt and the bottle are at rest. We can approach the bottle as one cylinder with radius ##R##, mass...

Homework Statement .A cylinder P of radius rP is being rotated at a constant angular velocity ωP along positive y-axis with the help of a motor about its axis that is fixed. Another cylinder Q of radius rQ free to rotate about its axis that is also fixed is touched with and pressed on P making...

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 Flywheels are large, massive wheels used to store energy. They can be spun up slowly, then the wheel's energy can be released quickly to accomplish a task that demands high power. An industrial flywheel has a 2.0 m diameter and a mass of 260 kg . Its maximum angular velocity...

Homework Statement A uniform cylindrical wheel of mass ##m_{1}## and radius ##R_{1}## rotates with angular velocity ##\omega_{1}##. It lies a certain distance (along the same axis) from a static wheel of radius ##R_{2}## and mass ##m_{2}##. The wheels are then pushed against each other with a...

Consider a hollow sphere roughly the size of the moon, spun up to produce 1g of centripetal acceleration along a band at its equator (about 15000 kph) Big stuff, I know. I have a few questions about the implication of such a system, and I hope someone can help me find some answers! - How tall...

Homework Statement A Texas cockroach of mass 0.17 kg runs counterclockwise around the rim of a lazy Susan (a circular disk mounted on a vertical axle) that has radius 15 cm,rotational inertia 4.9 ✕ 10^−3 kg · m2, and frictionless bearings. The cockroach's speed (relative to the ground) is 2.0...

Imagine a person is moving at the equator in the direction opposite of the Earth's spin. How long would it take them to stop the rotation of the Earth? Assume: the person's "weight" = 90.718 kg, they person's speed = 1m/s, The Earth's "weight" = 5.972*10^24 kg, the angular velocity of the...

Hello, I was recently given the task to find experimentally the moment inertia of a sphere. I thought of rolling the sphere down an inclined plane and applying conservation of energy to the sphere. The equations i came up with are: mgh = 1/2mv2 + 1/2Iω2 solving for v^2 we come up with the...

Homework Statement Two spheres are placed side by side on an inclined plane and released at the same time. Both spheres roll down the inclined plane without slipping. (a) Using FBD, explain what force provides the torque allowing the sphere to roll down the inclined plane. (b) Which sphere...

Homework Statement so I was going over my notes on classical mechanics and just started to review rotation matrices which is the first topic the book starts with. On page 3, I've uploaded the page here The rotation matrix associated with 1.2a and 1.2b is \begin{pmatrix} \cos\theta &...

Homework Statement Homework Equations Moment of inertia Torque Angular momentum The Attempt at a Solution I think I can understand the physics of the situation. There will be a torque on the bus due to gravity while the back of it remains in contact with the cliff and it will start to rotate...

Homework Statement Homework Equations RKE = .5iw^2 TKE = .5mv^2 U = mgh The Attempt at a Solution is my setup correct? mgh = RKE +TKE mgh = .5Iw^2 + .5mv^2 do i just total up the RKE and TKE for both the objects?[/B]

I'm trying to model a sphere having force applied at position P in the following diagram: I know that this applied force will have an x and y component; the y component will propel it upwards, but what I am confused about is the x component of the force. I know that the x component will propel...

Homework Statement Two blocks, m1 = 1.0 kg and m2 = 2.0 kg are connected by a light string as shown in the figure. If the radius of the pulley is 1.0 m and its moment of inertia is of the system is 5.0 kg*m^2, the acceleration of the system is (expressed as a fraction of gravitational...

Homework Statement A uniform rod (length = 2.4 m) of negligible mass has a 1.0-kg point mass attached to one end and a 2.0-kg point mass attached to the other end. The rod is mounted to rotate freely about a horizontal axis that is perpendicular to the rod and that passes through a point 1.0...

Hi, in the following problem, I need to find the inertia of the system. The axis of rotation passes through the center of mass ( the pink dot). I understand that I will be equal to 4(mr^2). However, I do not understand why r= 3 (6 divided by 2) and not sqrt13 ( half of the diagonal of the...

Homework Statement A grindstone is used to sharpen knives and consists of a stone cylinder and a central axle There are bearings between the axle and the frame to reduce any friction. This grindstone has a mass of 60 kg, a diameter of 0.600 m and has a moment of Inertia (I) of 4.50 kg.m2 ...

Homework Statement A block is placed inside a horizontal hollow cylinder. The cylinder is rotating with constant angular speed one revolution per second about its axis. The angular position of the block at which it begins to slide is 30° below the horizontal level passing through the center...

So I recently developed an interest in quad-rotors and was getting stated with its dynamics. I am particularly intrigued by the yaw motion of a quad-copter which comes into effect as a result of torques of the motors. When the motor torques are variable, we observe the yaw motion as result of a...

Homework Statement I have a rotating platform that spins as a mass attached to a wheel rotates the larger platform. The mass accelerates to the ground which spins the platform essentially. I am trying to calculate the moment of inertia of another mass which will be attached to the rotating...

Homework Statement A thin walled spherical shell with a mass of 0.605 kg and a radius of 0.0402 is released, from rest, at the top of an incline. The spherical shell rolls down the incline without slipping. The spherical shell takes 7.49 s to get to the bottom of the incline. A solid sphere...

Homework Statement A toy windmill consists of four thin uniform rods of mass m and length l arranged at rigth angles, in a vertical plane, around a thin fixed horizontal axel about which they can turn freely. The moment of intertia about the axel is ##I = \frac{4ml^2}{3}##. Initially the...

Homework Statement A homopolar generator consists of a metal disc of radius ##a## and a central axle which has radius ##a/4##. The disc has resistivity ##\rho## and thickness ##t##. It is rotated in a uniform magnetic field ##B## about an axis through the centre, which is parallel to ##B## and...

1. The problem statement, all variables, and given/known data Joe is painting the floor of his basement using a paint roller. A roller has a mass of 2.4kg and a radius of 3.8cm. In rolling the roller across the floor, Joe applies a force F= 16N at an angle of 35 degrees. What is the magnitude if...

Homework Statement A tangential force F acts at the top of a thin spherical shell of mass m and radius R. Find the acceleration of the shell if it rolls without slipping. Homework Equations Since the shell is rolling, friction does not act at the bottom. So equating the torque, F*R= I*α The...

Homework Statement How does Fr=Ialpha work and how is it applied to a pulley with one mass attatched? Homework Equations F * r = I * alpha I = moment of inertia The Attempt at a Solution I'm assuming F would be the tension of the pulley with the string. But how does that equation work? can...

Homework Statement You are asked to design an airplane propleller to turn at 2400 rpm. The forward airspeed of the plane is to be 75.0 m/s, and the speed of the tips of the propeller blades through the air must not exceed 270 m/s. What is the maximum radius the propeller can have? With this...

Homework Statement 2 masses are connected by a spring. They are on a frictionless plane inclined relative to the horizontal by ##\alpha##. The masses are free to slide, rotate about their center of mass, and oscillate. 1. Find the Lagrangian as a sum of the Lagrangian for the COM motion and a...

Homework Statement Consider a pulley with a mass-less cord attached to its edge. The rope hangs a distance of d= 2.50 m below the bottom of the pulley. Attached to the end of this cord is a block with mass 3.00 kg. There is also an electric motor attached to the pulley which supplies a torque...

I'm confused when it comes to the rotational version of Newton's Second Law: τ = Iα Is the torque τ the same thing as the moment of a force? I'm not sure if there is a discrepancy between British and American schools but I was always taught that a torque was a special case of moments and is...

When we say torque about a point what axis do we mean,how can rotational motion happen without an axis?

I know that to calculate the torque about an axis, we can choose any point on that axis and find the torque about that point and take the component along the direction of the axis.Buy what is the proof behind this theorem?

Homework Statement There is a object traveling at 0,2m/s with a mass of 75,000kg. The object impacts a fixed point at a distance of 3.5m from its center of gravity (COG) and rotates around this point. What is the reaction force at the point of rotation? Homework Equations I think it is...

Homework Statement The system looks like this: I have two discs which are connected. Disc 1 has ##R_1##(radius) and ##M_1##(mass) Disc 2 has ##R_2## and ##M_2## ## R_2 > R_1 ## ## M_2 > M_1 ## on both discs weights are attached on opposite sides. On smaller ##m_1## is pulling and on bigger...

Homework Statement A uniform bar AB of length L is freely hinged at one end A and released from a horizontal position. a) Find the initial angular momentum. Ans: 3g/2L b)Find the angular velocity when the bar is vertical. Ans: (3g/L)^(1/2) Homework Equations momentum of inertial of a rod...

1.) Homework Statement A Pulley System is shown below Find the accelerations of m1, m2 and m3 (such that there is no slipping between the disk and the rope.) Assume the threads to be massless. Homework Equations The Relevant equations i think are Newtons 2nd...

1. Homework Statement A small cube is sliding on a round dish (see attached figure) . The cube is always in contact with the (vertical) edge of the dish (which prevents the cube from falling outside the dish itself). There is friction between the cube and the dish. The dish can rotate around...

in rigid body dynamics is this relation between velocity of centre of mas and velocity of any particle in the rigid body correct? vcm = vp + rXω r is the position vector of the particle with respect to centre of mass relations are written in vector form and also tell me how to calculate...

Homework Statement A disc of mass M and radius r is kept on a horizontal,frictional plane and is connected to a horizontal spring at the centre.A particle of mass m strikes the topmost point of the disc,tangentially and sticks to it.Assume that the mass of the particle is m and it's velocity is...

This is of my own interest/ practice. Homework Statement A thin rod (of width zero, but not uniform) is pivoted freely at one end about the horizontal z axis , being free to swing in the xy plane (x horizontal, y vertically down). Its mass is m and its CM is a distance a from the pivot. The...

Homework Statement A disk roll without slipping down a incline plane. Identify the forces acting on the disk, explain qualitatively which of these forces do work. Homework Equations The rotational work is given by W=\int \tau_z d\theta (1) , where \tau_z is the component of the torque...

I have a doubt regarding the definition of rotational work, which is as follows W = \int \tau_z d \theta Where \tau_z is the component of the torque parallel to the axis of rotation z. My doubt concerns the fact that, looking at this definition, it seems that any torque which has an axial...

Homework Statement Actually, my confusion originated from solving two different problems... 1) A point object of mass 'm' moving horizontally hits the lower end of the uniform thin rod of length 'l' and mass 'm' and sticks to it. The rod is resting on a horizontal, frictionless surface and...

Homework Statement Respected Physics Gurus/experts...! I am confused in the application of Kinetic energy Expression, i.e, KE = (1/2)MVCM2+(1/2)ICMω2 I had been trying out this question actually(it's pretty simple though:-p)...--- "A rigid body is made of three identical thin rods each of...