Rotational Definition and 1000 Threads

Homework Statement A thin, light wire is wrapped around the rim of a wheel,. The wheel rotates without friction about a stationary horizontal axis that passes through the center of the wheel. The wheel is a uniform disk with radius R = .280m. An object of mass m=4.2kg is suspended from the...

Homework Statement A uniform square plate ABCD has mass 0.8 kg and side length .8 m. The square is pivoted at vertex D and initially held at rest so that sides AB and CD are horizontal (see the diagram). After it is released, the plate swings downward, rotating about the pivot point...

Hello fellow physicists, I have a query about a practical matter. I'm trying to simulate the rotational spectrum of a symmetric top and so far I've been able to produce a stick spectrum of it. My first problem is that the lines do not exactly match the positions of the peaks but my biggest...

Homework Statement A 75 g 30 cm long rod hangs vertically on a frictionless, horizontal axle passing through its center. A 10g ball of clay traveling horizontally at 2.5 m/s hits and stick to the very bottom tip of the rod. To what maximum angle measured from the vertical, does the rod with...

Homework Statement A 75 kg , 34 cm long rod hangs vertically on a frictionless , horizontal axle passing through its cener. A 15 g ball of clay traelling horizontally at 2.2m/s hits and sticks to the very bottom tip of the rod. To what maximum angle , measured from vertical , does the rod (...

Hi, I am trying to simulate a tangential force acting on a point on a structure and the corresponding opposing force caused by the moment of inertia of a mass at a different position. In this image the structure rotates around point c and there is a vector out of mass m opposing the...

Homework Statement A satellite follows an elliptical orbit. The only force on the satellite is the gravity atraction from the planet. The satellites speed at point A is 8000m/s, and it is 6000km away, Point B is 24000km east of the planet, and Point C is component vector 9000ikm+12000jkm...

Homework Statement An oxygen molecule consists of two oxygen atoms whose total mass is 5.3x10^-26 kg and whose moment of inertia about an axis perpendicular to the line joining the two atoms, midway between them, is 1.9 x 10^-46 kg*m^2. From this data, estimate the effective distance between...

From wikipedia: Rotating black hole So, the black holes have got the upper limit for rotating? Could somebody explain me why? I can understand one reason: due to special theory of relativity the event’s horizon’s circular/linear speed cannot be more than speed of light, right? Or maybe there...

Hi. I've been working on a project of angle stabilization for a vehicle moving along a string, looking like this: The propulsion system is connected to the central wheel, while the outer two wheels are used for support. I've observed that during acceleration the vehicle rotates. I...

Suppose I have a screw that makes some sort of frictionless ball bearing move at 0.3 m/sec That means that to find the RPM of the screw I do pi x mean diameter of the screw x rotation per minutes / 60000 and I get the answer?

Homework Statement Four rockets attached to a (wheel) space station exert a force of 65.5N to rotate it . The space station's angular velocity is increased at a constant acceleration of 3.63 x 10-3 rads-2. Each rocket is 11.2m away from the centre. Calculate the rotational inertia of the...

Homework Statement A disk with a mass of 4kg and a radius of 2m is free to rotate around an axis that passes through the center of the disk and perpendicular to the plane of the disk. The rotational kinetic energy of the disk is increasing at a constant rate of 20 J/rad; that is, the energy...

Hi, I am a little confused about the energy conservation of a pin ended free falling rod. When i try to derive energy conservation equation i am not sure including angular and linear velocity at the same time. I try to visualize the problem in the attached picture and put my derivation also...

Homework Statement I need to write the equations of motion for the mechanical system below. So I need to know how many velocities there are in the system, the answer key says there's only 4 but shouldn't there be 5? I am unsure if the J3 mass has it's own velocity from the point between K_2 and...

I have solved an exercise and I'd like to know if my proceeding about finding kinetic energy is correct or not, because this is the first time that I "meet" a situation like this. "A bar has mass M and length l. Its extremity A is hooked to a coil (with length at rest l0), its extremity B is...

so according to wiki: protons have a Lorentz factor of about 7,500 and move at about 0.999999991 c, or about 3 metres per second slower than the speed of light (c) If we consider speed of Earth's rotation or speed at which two galaxies approach each other (collision or otherwise)?

Homework Statement Answers were told to us to be F = 2.91 N Ft1 = 13.32 N Ft2 = 3.36 N Homework Equations Fx = Ft2 cos(θ) - F = 0 Fy = Ft2 sin(θ) + Ft1 - Fg = 0 Torque equation -FgDg - Ft2D1x cos(θ) + Ft2D1y sin(θ) = 0 The Attempt at a Solution I plugged in all of the information i had...

Homework Statement Given a rod of length 'l' placed upright on a smooth floor.A slight disturbance causes it to fall.Now required is the velocity with which the COM falls down when the rod makes angle θ with horizontal. The Attempt at a Solution now let the middle portion of the rod be...

1. A hoop with mass 2.0 kg and radius 1.5 m is rotating with initial angular velocity of 5.4 s-1. A disc with the same mass and radius is dropped on top of the hoop so that the centers coincide. What conservation law applies here? What assumptions must you make to apply it? What is the final...

I have two rigid bodies floating in space that are kinematically constrained by a joint (think of a 2 dof link mechanism floating in space). I have a body fixed reference frame on each rigid body plus the global space-fixed reference frame. The first rigid body is in the space-fixed...

Homework Statement We performed a small experiment in class which had us attach a mass to a string which hung on a pulley which led to a rotating object. We were then told to write down a conservation of energy equation stating that the initial energy is equal to the final energy. We were...

Homework Statement A 392-N wheel comes off a moving truck and rolls without slipping along a highway. At the bottom of a hill, it is rotating at 25.0rad/s. The radius of the wheel is .6m and its moment of inertia about its rotation axis is 0.800MR2. Friction does work on the wheel as it...

Homework Statement The professor gives us an exam preview where he hints at the types of problems via the picture. Attached is the preview. I have a question about pictures 1 and 2. It's probably a problem that involves rotational and translational energy, conservation of energy. If it's...

1. Problem statement 2. Related equations I = bmr^2 Energy equations (linear and rotational) 3. Attempt Part a) I know that the distance or height traveled by the box is [h - d] because center of the mass of box is just d. Initial kinetic energy of the box and cylinder is 0 and if only...

Homework Statement A constant force of 50 N is applied tangentially to the rim of a solid disc with a 60cm radius. The wheel has a moment of inertia of 40 kg m^2 a) what is the mass of the disc? b) 4 seconds after starting from rest, what angular speed does it have? c) How many...

Homework Statement Hey guys I have two questions. The first one I'm not sure, while the second one, I have some idea but don't know how to proceed with answering the question. 1. A rapidly spinning flywheel has been suggested as an energy storage mechanism for cars. Let's consider a 300kg...

Homework Statement We were given a video...I'm not sure if you can post video links otherwise I would...but it's a video of an airplane on a string flying in a circular motion. On the top of the string you can see that the tension of the string is 6.5N. and it is flying at an angle of 50°...

Homework Statement A uniform rod of length L1 and mass M = 0.75 kg is supported by a hinge at one end and is free to rotate in the vertical plane (Figure). The rod is released from rest in the position shown. A particle of mass m = 0.5 kg is supported by a thin string of length L2 from the...

Homework Statement Find the velocity with which a symmetric body of radius "R" starts to roll up an inclined plane if it was rolling without slipping on a horizontal plane with velocity "v1" and reached the incline. Angle of inclination of plane with horizontal=θ Radius of gyration of the...

I'm trying to learn some physics on my own, using the internet as my main source of information. Now, I'm a bit confused about some terminology, and I can't find anything about it... Distance vs displacement in rotational kinematics! Is there a similar difference as in linear kinematics...

Homework Statement A string passing over a pulley has a 3.80-kg mass hanging from one end and a 3.15-kg mass hanging from the other end. The pulley is a uniform solid cylinder of radius 4.0 cm and mass 0.80 kg. If the bearings of they pulley were frictionless, what would be the acceleration...

a)I used the equation KE=1/2Iw^2 I=mR^2 ---> 1.5x10^30*20000^2 w=2.1*2pi KE=1/2(1.5x10^30*20000^2)(2.1*2pi)^2=5.2x10^40 J t=2.1 rev/s / 1.4x10^-15 rev/s^2=1.5x10^15 seconds 5.2x10^40 J/1.5*10^15 seconds =3.4x10^25 watts B)1.15*10^15 s=1.1*10^18 years I feel like this method is...

Homework Statement A uniform rod of length "L" is kept vertically on a smooth horizontal surface at a point "O". If it is rotated slightly and released, it falls down on the horizontal surface. To what distance will the lower end of the rod "shift" from point "O" ? Note : The answer in the...

Here is a text from my Physics Book : The net external torque on the object about any axis must be zero for it to be in rotational equilibrium. I divide the torques into two categories, anticlockwise and clockwise. (This approach works fine for 2-D objects but will it work for 3-D objects...

Homework Statement In throwing a hulahoop with back spin, you toss the hoop to the right, and it (1) moves right with speed v0, but rotates ccw with speed ω0. At some point, O, (2) it will change direction, and at that point it will start moving to the, left, but still be sliding because it...

This is not a homework question. An adult exerts a horizontal force on a swing that is suspended by a rope of length L, holding it at an angle θ with the vertical. The child in the swing has a weight W and dimensions that are negligible compared to L. The weights of the rope and of the seat...

Homework Statement A quarry crane is used to lift massive rocks from a quarry pit. Consider the simplified model of such a crane shown in the figure. (Figure 1) The ends of two poles are anchored to the ground at the same point (point O). From this point, one pole rises vertically and the...

Hey guys, So, I'm kinda distraught over this problem because, by all accounts, I should be able to get the problem no sweat. However, it just hasn't been happening. If you could point out my flaw, I would truly appreciate it! In the problem, we are asked to find the magnitude of the...

Homework Statement Consider a sphere that is placed at a table. The coefficient of kinetic friction between the sphere and the table is μ. At time t = 0, the velocity of the center of mass of the sphere is Vo = 0, and the sphere is rotating with respect of the horizontal axis with angular...

Homework Statement Show that if a Hamiltonian H is invariant under all rotations, then the eigenstates of H are also eigenstates of L^{2} and they have a degeneracy of 2l+1. Homework Equations The professor told us to recall that J: \vec{L}=(L_x,L_y,L_z)...

A mine cage of mass 4 tonne is to be raised with an acceleration of 1.5m/s^2 using a hoist drum of 1.5m diameter. The drum’s mass is 750kg and its radius of gyration is 600mm.The effect of bearing friction is equivalent to a torque of 3kNm at the hoist drum. What isthe driving torque required...

Homework Statement A ball of clay of mass m travels with velocity v in a path tangent to a disk of radius R and mass M. The clay collides with the disk tangentially to its outer rim ( a totally inelastic collision) and the clay and disk begins to spin about the axis. a) What is the final...

Edit: Nevermind, solved it. Homework Statement A ceiling fan with 80 cm-diameter blades is turning at 60rpm . Suppose the fan coasts to a stop 25 s after being turned off. What is the speed of the tip of the blade 10 seconds after being turned off? Through how many revolutions does the fan...

I was thinking about the rotational kinetic energy of fluids the other day and I realized that I have a huge gap in my knowledge of physics. Why doesn't rigid body rotational kinetic energy (KE = 1/2*I*ω^2) not apply to fluids or deformable bodies (it should at least be proportional to that...

Hi PF! I've been working on a research problem involving fluid dynamics, and I'm currently looking at a "bathtub flow". This is where water is draining through a hole, and we have a vortex. In a paper I have found dealing with this flow, the velocity potential was written as: \psi = Alnr + B\phi...

Homework Statement If we shift the rotation axis from the center of mass of an object, with no change in the orientation of the axis, what happens to the rotational inertia of the object around the axis? Homework Equations Calculating the Rotational Inertia The Attempt at a Solution Does it...

Homework Statement An green hoop with mass mh = 2.6 kg and radius Rh = 0.12 m hangs from a string that goes over a blue solid disk pulley with mass md = 2.3 kg and radius Rd = 0.09 m. The other end of the string is attached to a massless axel through the center of an orange sphere on a flat...

First, energy of a disk: \int \frac{dm}{2}r^2 \omega^2 =\frac{\omega^2}{2}\int_0^R m\frac{2 \pi r dr}{\pi R^2}r^2 =\frac{m\omega^2}{ R^2}\int_0^R r^3 dr=\frac{m\omega^2 R^2}{4 } Which agrees with other sources. However, in the following lies my problem: The equation for a circle...

Hello! How do I calculate the maximum possible rotational speed of a thin walled hollow cylinder? In other words, at what rotational speed will it explode due to centripetal force? This picture shows the plane of rotation...