Homework Statement
Find the mass, M, of a rotating wheel of radius r that has an attached mass, m, suspended by a string using conservation of energy. The mass is suspended a height, h, above the ground and it takes a time of t seconds to reach the ground.Homework Equations
U_g,mass = K_f,mass...
A real incompressible fluid is contained in the region between two coaxial cylinders of radii R1 and R2. The outsider cylinder rotates with angular velocity w, in stationary regime, and the flow is purely circular. Neglect the action of gravity.
a) Show that vφ (azimuthal velocity component)...
According to Einstein (e.g. in his book The Meaning of Relativity), a clock rotating about a central clock will be judged by the central clock to run slower than the central clock.
This means that a signal sent by the central clock will be perceived by the rotating clock as being of a higher...
Homework Statement
A solid rubber wheel of radius R and mass M rotates with angular veloctiy \omega_0 about a frictionless pivot. A second rubber wheel of radius r and mass m, also mounted on a frictionless pivot, is brought into contact with it. What is the final angular velocity of the first...
Homework Statement
PROBLEM:
You have a horizontal grindstone (a disk) that is mass m, has a radius r, and is turning at f in the positive direction. You then press a steel axe against the edge with a force of F in the radial direction.
RANDOMIZED VARIABLES:
m= 95 kg
r= 0.33 m
f= 92 rpm
F= 25...
Homework Statement
So this isn't a homework problem but I don't know where else I am supposed to post for general help. I am basically trying to understand the derivation for the equation of motion of a particle in a rotating frame. See attachment for derivation and which steps I am stuck on...
Homework Statement
A small body A is fixed to the inside of a thin rigid hoop of radius R and mass equal to that of the body A. The hoop rolls without slipping over a horizontal plane; at the moments when the body A gets into the lower position, the center of the hoop moves with velocity v0...
Does a point charge 'q' (say an electron) moving with constant angular speed ω in a circle of radius R constitute a current ?
A rotating ring of uniform charge density is treated as a current flowing in the ring .
On similar lines I think a point charge q is equivalent to current given by i =...
Homework Statement
Hello everyone.
Each minute, I have 3d coordinates of points at the surface of a unit sphere (with center at (0;0;0)) rotating with an axis which can (slightely?) change over time. I want to know the linear speed (s) of this sphere. I don't know how to find r at each time...
Okay, so, we have
y=2/x, y=0, x=1, x=3 and it's rotating around y=-1
As I understand it... This means
(2/x +1)^2-(0+1)^2
(4/x^2 + 4/x)
The integral of that is
-4/x + 4ln(x)
Am I right so far?
Plug in the 3, and then the 1
-4/3 + 4ln(3) - -4+4ln(1)
Then the result of that is multiplied...
Homework Statement
Two pucks of mass m slide freely on a horizontal plane. They are connected by a
spring (constant k and negligible un-stretched length) and set in circular motion
with angular momentum L. The pucks are given a small, simultaneous radial
poke. What is the frequency of...
Homework Statement
A disk rotates with constant angular velocity \omega. Two masses, m_A and m_B, slide without friction in a groove passing through the centre of the disk. They are connected by a light string of length l, and are initially held in position by a catch, with mass m_a at a...
A load of mass 250kg is required to be lifted by a means of a winding drum and cable. The mass will be initially at rest, accelerated uniformly upwards for 4 seconds and then decelerated uniformly for one second. such that a final height of 10.5 metres is gained.
The winding drum has a mass...
Homework Statement
A mouse starts running on a circular path of Radius = 28m with constant speed u = 4m/s. A cat starts from the center of the path to catch the mouse. The cat always remains on the radius connecting the center of the circle and the mouse and it maintains magnitude of its...
Homework Statement
Hello everyone,
How do I go about this problem; Describe the motion of the particle, m, inside the rotating tube. (See attachment please.)
At time t=0, r(t=0)=b and \dot{r}(t=0)=v_{0}
Homework Equations
I think it would be practical to use polar coordinates to describe...
Homework Statement
A metallic chain with a length ‘l’ andd whose ends are joined together is fitted onto a wooden disc as shown in the figure.The disc rotates with a speed of n revolutions per second.Find the tension of the chain T if its mass is m.
Homework Equations
The Attempt at a...
Homework Statement
Hi everyone!
I'm struggling to understand how to solve this problem, I searched on the web, but I didn't find anything similar.
I have a motor delivering a power P=5kW at n=1500rpm. This motor is mounted on 4 supports, each having a rigidity k=15kN/m. I know that distance...
I am referring to "Newton's bucket" -- essentially a hollow cylinder filled with water inside which rotates about the cylinder's axis. The result is that the surface of the water is a parabola. The argument for this is that the surface normal of the water must be directly opposing the other...
Hi,
I'm looking for the Moment Coefficient (Cm) for a 3D Rotating Cylinder, this means, I there is a free stream of fluid and there is inmerse a cylinder rotating about its own axis , and also rotating about an axis parallel to the free stream.
I found in the book of Peter Childs, called...
I am sure this is not the best description of the problem, so let me know how I can clarify.
Say there are 2 coordinate systems, with one orbiting around the other. Call one fixed ƒ and the other rotating ρ. The goal is to find the transform between the two frames.
What's known is
1) A...
Homework Statement I have attached the problem as a picture on this post, am really really unsure on how to start!
so far the only thing i can think of doing is using this equation
(\frac{d^{2}r}{dt^{2}})_{s} = ( \frac{d^{2}r}{dt^{2}})_{s'} + 2ω \times (\frac{dr}{dt})_{s'} + \dot{ω}...
Hi Everyone,
Suppose that we have cylindrical coordinates on flat spacetime (in units where c=1): ##ds^2 = -dt^2 + dr^2 + r^2 d\theta^2 + dz^2##
I would like to explicitly calculate the expansion tensor for a disk of constant radius R<1 and non-constant angular velocity ##\omega(t)<1##. I...
Homework Statement
The rotating parts of a motor have a moment of inertia of 15 kgm^2 and an optimum running speed of 1400 rev/min. When operating the motor is connected at optimum speed , by means of a clutch, to a shaft which has a counter rotation of 600 rev/min. The shaft has a mass of...
I was solving this paper, but got stuck on this question, and it's been bugging me endlessly. I don't know what I'm missing. Here's the question:
A rod of 20 dia is fixed to the ceiling of a roof on one end. A rotor of 50 kg mass is attached to the free end with bearings. The CG of the rotor...
Homework Statement
for this question, since area of cutting of magnetic field change, so magnetic flux change, f is unchanged . but i don't understand why the torque will change since the force is unchanged, since torque=FORCE X DISTANCE FROM THE ROTATING PIVOT
Homework Equations...
I'm reading Lanczos: 'The variational Principles of Mechanics'. I need help resolving a paradox - which is probably trivial…
Lanczos (page 100 Dover edition) introduces a system, S', rotating at angular velocity \vec \Omega about an axis through a fixed point with respect to inertial system...
This problem is from Boas Mathermatical Methods 3ed. Section 16, problem 1.
Show that if the line through the origin and the point z is rotated 90° about the origin, it becomes the line through the origin and the point iz.
Use this idea in the following problem: Let z = ae^iωt be the...
Suppose that a wheel is rotating around its axis in free space with no friction, with no external forces acting on it. In theory, the wheel will rotate forever with constant angular velocity. This velocity is assumed to be small (essentially non-relativistic).
Now, consider an observer O...
Homework Statement
A thin copper (resistivity 1.7 x 10-8 Ωm, density 8.9 g/cm3) ring rotates about an axis perpendicular to a uniform magnetic field B0. Its initial frequency of rotation is ω0. Calculate the time it takes the frequency to decrease to 1/e of its initial value, under the...
Homework Statement
a disk of radius 40 cm is rotating about an axis through its centre. the moment the inertia of the disk is 0.015 kg m^2 and it is turning at 3 rev/s. sand falls on the disk at a distance of 20 cm from the axis and builds a 20 cm radius sand ring on the disc. How much sand...
Homework Statement
I have to find current absolute acceleration in attached picture in points 1,2,3,4 and draw vectors.
The picture is rotating pendulum. The rest data show attached picture:
Homework Equations
aabs = arel + au + acor
acor=2*angular velocity X vrel
The Attempt at a...
Homework Statement
Introduction to Classical Mechanics by David Morin - problem 9.43, page 424
A uniform flat rectangular sheet of mass m and side lengths a and b rotates with angular speed w around a diagonal. What torque is required? Given a fixed area A, what should the rectangle look...
Suppose you have a body floating in a rotating superfluid. Maybe a speck of dust. Would it rotate?
What if you have two bodies connected in some way. Would this system rotate around its center of mass?
Homework Statement
A uniform disk of mass 2M, radius R, is mounted on a frictionless horizontal pivot through its principal axis. The disk has an additional point-mass, M, fixed to a point on its circumference.
(a) Give the Lagrangian for this system.
(b) Find the frequency of small...
Homework Statement
A body with mass ##m## can move without any friction on ellipse that ##(x/a)^2+(y/b)^2=1## describe. In ##y## direction homogeneous gravity field ##g## is present. For generalized coordinate we take angle ##\alpha ## defined with ##x=acos\alpha ##, ##y=bsin\alpha ##. Find...
Homework Statement
Around vertical axis ##O## a body on picture below (see attachment) is being rotated with constant angular velocity ##\Omega ##. On the circle we have a body with mass ##m##, that can feels no friction. Find position of that body as function of ##\phi ## and time. Calculate...
Homework Statement
I'll provide picture for clearer understanding. The solid cylinder of mass ##m## and radius ##r## revolves about its geometric axis at an angular rate ##p## rad/s. Simultaneously, the bracket and shaft revolve about x-axis at the rate ##\omega## rad/s. Determine the angular...
Homework Statement
So let's say I have a particle moving at some given latitude λ on or near the Earth's surface, northen hemisphere (see diagram attached). Look at the coordiate system I have x',y'and z' with origin on the surface...and the velocity I'm given has components along those primed...
Homework Statement
I'll provide a picture for clearer understanding. The problem is to calculate the angular momentum of the rod rotating about the z-axis. I have serious difficulties in deriving the inertia matrix, that's all I need help with.
Progress
Since the rod is...
Hello,
I have a project whereby I am designing a toy that spins a horizontally positioned propeller, then releases it.
After releasing it, the propeller gains height, but moves somewhat away from the operator of the toy.
Is the direction of airflow through the propeller vertically? If...
Question on Acceleration of Rotating Objects:
The Physics Textbook I have says that the Acceleration of a spinning object is the Pythagorean-theorum result of sides for Centripetal-Acceleration (toward the rotation center) and Tangential-Acceleration (perpendicular to Centripetal-Acceleration...
Homework Statement
Hi, everyone. Me again. This time I'm here to ask about the tension in the string on a massive pulley.
We have a wheel of radius R with a moment of inertia about its principal axis of 2/3 MR2 , suspended above the ground on frictionless bearings. A massless string of...
Homework Statement
Consider a non conducting ring of radius r and mass m which has a total charge q distributed uniformly on it.The ring is rotated about its axis with an angular speed ω.
a)Find the equivalent electric current in the circuit.
b)Find the magnetic moment μ of the ring...
Homework Statement
A horizontal 845.0 N merry-go-round with
a radius of 4.3 m is started from rest by a
constant horizontal force of 74.0 N applied
tangentially to the merry-go-round. Find the
kinetic energy of the merry-go-round after
2.2 s. Assume it is a solid cylinder. The...
Homework Statement
A copper wire loop is initially at rest in a uniform magnetic field (full flux going through it). Between times t=t1 and t=t1+(delta)t the loop is rotated about a vertical axis as shown (no flux going through it). Will current flow through the wire of the loop during this...
Homework Statement
A massless spring of length b and spring constant k connects two particles of masses m_1 and m_2 .
The system rests on a smooth table and may oscillate and rotate.
a) Determine the Lagrange's equations of motion.
b) What are the generalized momenta associated with...
Homework Statement
I am basically designing a rotary drum dryer and need to know the positions of the bearings for the dryer to be stable.
The drum is of length 17 m with diameter 3.24 m, inclined at 2° rotating at 3.24 rpm. I need to find the distance X and OY. (Given that Y passes through...
Homework Statement
A 75g mass sits 75cm from the center of a rotating platform undergoing a uniform angular acceleration of 0.125rad/s . The coefficient of static friction between the mass and the platform is 0.250. What is the speed of the mass when is slides off?
A. 0.889 m/s
B. 1.26...
As I've red, different points on the rotating disk, or rotating object have different velocities and so they should time dilate differently. Points on equator are for instance quicker than those in Scandinavia. When we take an inertial frame that has zero velocity with respect to the Earth as a...