What is Rotaional kinematics: Definition and 19 Discussions

Hello, I understand the equation that describes the angular accelerator when 3 reference frames are involved is: Now I would like to ask what is the resulting equation when accounting more than 3 reference frames, i.e. when n-reference frames are involved. Thank you.

The question is: A uniform rod of length ##L## stands vertically upright on a smooth floor in a position of unstable equilibrium. The rod is then given a small displacement at the top and tips over. What is the rod's angular velocity when it makes an angle of 30 degrees with the floor, assuming...

Here is the problem statement along with the figure. Here, I take the right-ward and anti-clockwise directions to be positive. After the ball collides with the wall, its angular velocity remains the same and its velocity changes direction while remaining the same in magnitude. Using the...

I have tried to use the intial velocity v=(2gH)^(1/2) and tried to use conservation of energy, using potential energy to find the maximum height but still can't arrive to the answer provided. Don't know what concepts are relevant here, apparently I can't use velocity neither cosine or sine. I...

Suppose a cylinder is launched on a horizontal frictional surface such that it has initial translational velocity v and zero angular velocity .the kinetic friction would be applied between the contact points of the cylinder and the surface, opposite to the direction of the translational motion...

I was pondering my practice of talking about circular motion in the horizontal direction and the vertical direction. But I'd often would see in books, notes, and the internet that we assume constant velocity for the vertical case. However, when one thinks about the forces at different points in...

The answer here is A What i did is getting the area as follows, 2×4×1/2 +3×-6×1/2 +4×-6 = -29 and then use this Δω=ωf-ωi -29=ωf-5 ωf=24 but there is no such choice.

I refer to the website below (for more information): http://www1.lasalle.edu/~blum/p106wks/pl106_Pendulum.htm#:~:text=The forces acting on the,the tension of the string.&text=The net radial force leads,is v2/r.) P.S. I'll insert my specific questions in the following paragraphs in this format...

A single pair of points will be in contact between P and Q. The frictional force will try to make the velocity of these points equal. Say the final angular velocity of Q is ωq. The velocity of points in contact can never be equal because of difference in directions of ωq and ωp. If I break...

Firstly I only consider one of the wheels. This wheel consists of a big wheel (black) with mass M and radius R and inside it a circular region with a negative mass (-m) and radius R/2. (I assume they have same mass density but with opposite signs. I do this because I don't know where the center...

As shown in figure there's a homogeneous solid sphere. It is rotating about axis which is passing through point P directed perpendicular to the plane of paper. (In short like a pendulum). I'm neglecting gravity and assuming a force F which is directed perpendicular to the string. (The string...

Homework Statement A uniform rod is released on a friction-less horizontal surface from rest. Initially, the rod makes an angle θ = 60° with the horizontal. What is the acceleration of the center of mass of the rod, just after release? Homework Equations Torque = Moment of Inertia × Angular...

Homework Statement Homework EquationsThe Attempt at a Solution i just don't know from where to take the R which is colored with brown, in the 2(MR^2), what is the R here exactly, because i took the radius of the sphere , but i get different answer althought it's near.

If talking about a particle rotating around an axis away from it by r. if the particle is moving with constant angular velocity ω. is the linear velocity constant or no? Now what I know is that since we have Vt= ωr, so r doesn't change, as well as ω, so Vt is said to be constant. but I think...

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 [/B] A particle P1 moves with a constant velocity v along x-axis, starting from origin. Another particle P2 chases particle P1 with constant speed v, starting from the point (0, d). Both motion begin simultaneously. Find - 1. Initial acceleration of P2. 2. Ultimate...

Homework Statement I am trying to figure out what torque is applied to 2 wheels counter-rotating at 4,000 rpm when a tennis ball is squeezed between them and then propelled forward (because the wheels are counter-rotating).This is how a tennis ball machine propels a ball forward. I know the...

I have 2 ellipsoids: Ax^2/a^2+Ay^2/b^2+Az^2/c^2=1; (*a,b,c>0 constants*) Bx^2/a^2+By^2/b^2+Bz^2/c^2=1; Ellipsoid A rotates around axis [wax;way;waz] (unit vector) with an infinite speed; Ellipsoid B rotates around axis [wbx;wby;wbz] (unit vector) with an infinite speed; [Dx;Dy;Dz] is the vector...

Homework Statement The shows an arrangement of 15 identical disks that have been glued together in a rod-like shape of length L = 1.0000 m and (total) mass M = 100.0 mg. The disks are uniform, and the disk arrangement can rotate about a perpendicular axis through its central disk at point O...