Rotation Definition and 1000 Threads

This question is from 1977 AP Physics C so I suppose it would be clear enough, but I am confused about question c. Question a is easy (it rotates counterclockwise), question b too (Στ=6*rxF=6*r x (I*i x B)=0.06). Question C is where I am stuck. The diagram provided with the question looks like...

Commutativity for planar rotations follows from a direct calculation. What does 'direct calculation' mean?

$$mg(0.45) = mg(R + R \cdot cos(\frac{π}{3})) + \frac{1}{2}mv^2$$ $$v^2 = g(0.9 - 3R)$$ The centripetal acceleration during the "flying through air" will be given by gravity $$mg \cdot cos(\frac{\pi}{3}) = \frac{mv^2}{r}$$ $$R = \frac{1.8}{5}$$ But my book says $$ R = \frac{1}{5}$$

Homework Statement A car initially traveling at 29.0 m/s undergoes a constant negative acceleration of magnitude 1.75 m/s2after its brakes are applied. (a) How many revolutions does each tire make before the car comes to a stop, assuming the car does not skid and the tires have radii of 0.330...

how much rotation needs to start volume flow for a adjustable variable pump?.I get it 5pi from the book. Is there any rule that it needs such rotation to start volume flow. From where I get it?I think that pump designer does not give the information on the manual.

Hi all, The scenario I'm considering is a solid sphere (of uniform density) rotating with constant angular velocity when it abruptly splits into two hemispheres along a cut which contains the rotation axis. The hemispheres will begin to separate; if, for example, we consider the rotation to be...

Is it difficult to show that a Fermi-Walker "rotation" happens only in the plane formed by a particle four-acceleration and four-velocity?

in the case of a disc rotating about the centroidal axis and having an unbalanced mass we used the formula F(force)=m x r x w^2, where r is the distance from the center to the center, m mass of the unbalanced, w rotational speed in the case of a disc rotating about axis parallel to the...

This is a question about the concepts behind rigid body rotation when we use relative velocity. In general, let us say that we have a rigid body and on it are two points, A and B, which are moving with velocities vA and vB respectively. These velocities are in random directions. The theory...

If gear 1 fits into the internal gear and is made to rotate, will the internal gear rotate with gear 1? https://imgur.com/gallery/ELYZoRb

Problem : A cylinder of mass ##M## and radius ##R## rotates with an angular velocity ##\omega_1## about an axis passing through its centre of symmetry. Two small masses each of mass ##m## (small in comparison to the radius of the cylinder) are glued to either of the two circular faces of the...

Given the coordinates ##P = (3,4)## , find the coordinates of ##P"(x',y')## when the origin is shifted to (1, –2), and the axes are rotated by 90° in the clockwise direction. I attempted to solve this problem using the following formulas : ##x = X + h## and ##y = Y + k## for translation of the...

I am trying to understand the picture below which is of a contractible and uncontractible loop in what I would call (proper name?) "rotation space", where "rotation space" is a solid ball of radius π with opposite points on the surface of the ball identified, each point of the ball representing...

Recently I have studied that from the rotation curve of spiral galaxies, the nearly constt. behaviour of velocity of the stars situated far away from the central core suggests mass(r) ~ r ,rather than 1/√r as expected. Are there any other theory which proves the existence of dark energy ??

Hi all, This isn't really "homework" - it's a personal project I'm working on. I'm attempting to animate some mechanical controls of a turbine engine in Adobe After Effects. Having a hard time with the math for "rotating two interconnected points". Here is a photo for visual aid: It's...

This question is about the general 1 loop correction to the propagator in QFT (this is actually not important for this question). Let's say we have an integral over an integration variable x, and this x ranges from ##-\infty## to ##\infty##. If we look at this integration contour in the complex...

Homework Statement A body is thrown as shown in the picture (0°<x<90°). In what direction the body will the body move in relation to the point it was thrown from - east or west (assume the distance between the point the body was thrown from and the point it lands at is no more than a few...

Hello everyone, A rigid body is a system whose points, pairwise, always keep a constant mutual distance. Let's say the body is in a certain configuration ##C_0## at time ##t_0## (which means that each point has a specific velocity and position relative to a fixed lab reference frame) and the...

Homework Statement [/B] The problem consists of deriving the matrix for a 3 dimensional rotation. My approach consisted of constructing an arbitrary vector and rewriting this vector in terms of its magnitude and the angles which define it. Then I increased the angles by some amount each. I...

I was looking at the numbers regarding the planets in our solar system, their bulge, their flattening ratio and their rotational speed. I know that rotational speed plays a role in this flattening, however what else is at play? For example, Earth's flattening ratio is nearly 1:300, whilst Mars...

When a ship heels, the centre of buoyancy of the ship moves laterally. It might also move up or down with respect to the water line. The point at which a vertical line through the heeled centre of buoyancy crosses the line through the original, vertical centre of buoyancy is called the...

I am exercising on Stellar Physics topics and in particular the questions below: 1) First of all on the rotation profile for the radiative zone: I know that unlike the convective zone, where the rotation varies mainly in latitude (faster at the equator than at the poles), the radiative zone...

Homework Statement A rigid cube in the figure moves in space. At a certain time ##t## its front face ##ABCD## is vertical and the velocity of vertex ##A## is vertical down ##v## while the velocity of its vertex ##D## makes an angle with the vertical and has magnitude ##v_{2}## while lying on...

Homework Statement A car is lifted vertically by a jack placed at the car's rear end 40cm off the central axis, so that the weight of the car is supported by the jack and the two front wheels. The distance between the front wheels is 1.60m, the distance from the axis connecting the two wheels...

Hello, I was struggling with solving a specific integral. I know that I can rewrite the exponential matrices and the range of the three Euler angles. However, I am not sure I should I write in terms those three Euler angles.

Homework Statement A 23 kg solid door is 220 cm tall, 95 cm wide. What is the door's moment of inertia for rotation about a vertical axis inside the door, 17 cm from one edge? Homework Equations I = I_cm + MR^2 The Attempt at a Solution I = I_cm + MR^2 I = (1/12)(23kg)(0.95m)^2 +...

I have been reading this article https://tritonstation.wordpress.com/2018/10/05/it-must-be-so-but-which-must/ so why does Mond fit so well over dark matter models?

Homework Statement A 100 g ball and a 250 g ball are connected by a 34-cm-long, massless, rigid rod. The balls rotate about their center of mass at 150 rpm . Homework EquationsThe Attempt at a Solution I solved by first getting the center of mass, then converting rpm into m/s I treated rigid...

Homework Statement In the figure below, a constant horizontal force app of magnitude 18 N is applied to a uniform solid cylinder by fishing line wrapped around the cylinder. The mass of the cylinder is 19 kg, its radius is 0.11 m, and the cylinder rolls smoothly on the horizontal surface. (a)...

Homework Statement A uniform rod of mass M and length l is hinged at the center. a particle of mass m and speed u sticks after hitting the end of the rod. find the angular velocity of the rod just after collision Homework Equations Energy conservation-0.5mu^2=0.5(m+M)v^2 Angular momentum...

Homework Statement Homework Equations torque= F*r*sintheta total force on y= 0 The Attempt at a Solution how come it will rotate in this situation?? espicially that he is ignoring the weight force of the rod! i knew that i ignored the mass of the rod when he said total force on y= F -F. if...

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 A force is applied tangentially to a rigid body on a horizontal surface.if it doesn't slip find the frictional force https://ibb.co/m9sMEU Homework EquationsThe Attempt at a Solution The solution tells us to take axis about the bottommost point in contacy with the surface...

for compute: $$e^{\frac{iS_z\phi}{\hbar}}S_x e^{\frac{-iS_z\phi}{\hbar}}$$ so, if we use $$S_x=(\frac{\hbar}{2})[(|+><-|)+(|-><+|)]$$ $$e^{\frac{iS_z\phi}{\hbar}}(\frac{\hbar}{2})[(|+><-|)+(|-><+|)] e^{\frac{-iS_z\phi}{\hbar}}$$ so, why that is equal to...

Here's some basic mechanical engineering question for you guys. How can one turn a press of a button (or pulling) into a rotation? My goal is to be able to have the button in any orientation and position and still be able to rotate a dial 360 degrees when fully pressed/pulled by 5mm. I suspect...

http://www.animations.physics.unsw.edu.au/jw/rotation.htm#rolling I have set up an apparatus similar to what the above link says (the first bit about brass object with shaft). So basically, the shaft is in contact when the brass is first rolling, then it suddenly accelerates when the edge of...

In Mathematical Methods for Physicists, 6th Edition, by Arfken and Weber, Chapter 1 Vector Analysis, pages 8-9, the authors make the following statement: "If Ax and Ay transform in the same way as x and y, the components of the general two-dimensional coordinate vector r, they are the...

From NASA page: The inner parts of the rings move around Saturn faster than the outer parts, all in accordance with Kepler’s third law for small objects revolving about a massive, larger one. They orbit the planet with periods ranging from 5.8 hours for the inner edge of the C ring, to 14.3...

For illustration purposes, I have attached an image of the line with the angle that I want to calculate. I am trying to determine the angle of rotation and the calculation that I am using currently is as below: angle = math.atan2(y,x) I use this formula to calculate the rotation for A and A'...

Are there any good theories which can explain how the orbits of planets are not aligned with the rotation of the Sun? I gather there is about 6 degrees of differance, which is not small.

So I'm looking at a problem that involves a situation that looks like this the cylinder rolls without gliding. And there are these following equations that apply to it (1) mg - T = ma (for the block hanging vertically) (2) T + f = Ma (for the cylinder f = friction force, T = String force) (3)...

Homework Statement Because Earth's rotation is gradually slowing, the length of each day increases: The day at the end of 1.0 century is 1.0 ms longer than the day at the start of the century. In 61 centuries, what is the total of the daily increases in time (that is, the sum of the gain on the...

Homework Statement [/B] A thin cylindrical rod with the length of L = 24.0 cm and the mass m = 1.20 kg has a cylindrical disc attached to the other end as shown by the figure. The cylindrical disc has the radius R = 8.00 cm and the mass M 2.00 kg. The arrangement is originally straight up...

Homework Statement Homework Equations orthogonality condition: that means that the point of ICR is orthogonal to the velocity Vb and Va The Attempt at a Solution the solution that i found with the problem is: The ICR of the bar is at infinity. the motion of the bar is translational. I think...

Hello, I come across a problem in programming and I do not find a lot of help on the internet, so I hope I can find an answer here. I have a 3D array representing a function, say f(i,j,k) and a basis function u(i,j,k). I would like to perform a general rotation of the basis function u so that I...

I am trying to solve problem number 4 part A and B from (http://people.physics.tamu.edu/kamon/teaching/phys218/exam/2003C/2003C_Exam3_Solution.pdf) but I am confused about certain aspects of it. In part A, I understand that since we are considering the person as a cylinder, the equation for...

I have some questions about torque and its role in gymnastics, or with anything that may rotate, possibly. First, is it possible for someone or something to use torque to rotate in two different axes of rotation at once? In a separate situation, is it possible to tilt using torque to tilt the...

Hello, I'm having a visualisation problem. I have a point in R3 that I want to rotate about the ##y##-axis anticlockwise (assuming a right-handed cartesian coordinate system.) I know that the change to the point's ##x## and ##z## coordinates can be described as follows: $$z =...

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...

Homework Statement A uniform bar of mass m is being moved on a smooth horizontal plane by applying a constant horizontal force F acting at the lowest point. If the rod translates making a constant angle 'theta' with vertical, the value of F must be? Homework Equations 1) F=ma 2) Torque=Moment...