What is Rotating bodies: Definition and 25 Discussions
A rotating frame of reference is a special case of a non-inertial reference frame that is rotating relative to an inertial reference frame. An everyday example of a rotating reference frame is the surface of the Earth. (This article considers only frames rotating about a fixed axis. For more general rotations, see Euler angles.)
TL;DR Summary: What should be the geometries of two contacting solids that may have a relative rotation and translation along the same axis?
a) Consider two rigid bodies that have a relative motion characterized by a rotation and a translation with respect to the same axis (like a bolt and a...
Simple question. Let's say a solid cylinder has an initial speed ##v_o## and it's rotating on infinitely hard ground without air resistance.
The cylinder will come to a stop eventually. There are two sources of friction.
Since the wheel/cylinder is deformed at the contact patch, there is some...
The total force acting on the pulley is zero so:
F=mg+T1+T2 (1)Analyzing the torque and angular acceleration about the actual axis of rotation, the axle of the pulley, gives:
τnet=T1R−T2R=Iα (2)If we analyze about point P, the right edge of the pulley where T1 is applied, we get...
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...
I have tried this same approach three times and I got the same answer. I can't figure out what's wrong. Btw answer is 12mu/(3+cos2α)
And yes, sorry for my shitty handwriting. If you can't understand the reasoning behind any step then please let me know.
The acceleration and velocity of a body rolling down without slipping on a frictionless inclined plane are given by
$$
a=\dfrac{mg\sin \theta }{m+\dfrac{I}{r^{2}}}=\dfrac{g\sin \theta }{1+\dfrac{K^{2}}{r^{2}}} \cdots(1)
$$
$$...
1) To be in equilibrium, it must be $$\begin{cases}F_{centr}-T=0\\ T-mg=0\end{cases}\Rightarrow F_{centr}=T=mg\Rightarrow m\omega^2 R_0=mg\Rightarrow R_0=\frac{g}{\omega^2}$$
2) It is intuitive that this equilibrium is unstable but I don't know how to formally prove this.
3) In ##R_0## the...
I've a disc which can rotate freely about two perpendicular axis (fixed to the body)
If I simultaneous try to rotate it about the two axis, what will happen?
The conservation of energy equation is basically GPE is converted to KE of block and KE of cylinder.
To get the correct answer, the KE of the cylinder is 1/2mv^2, where m is its mass and v is the velocity of its COM (which is the centre of cylinder).
However, I viewed the cylinder as rotating...
$$\tau = I\alpha$$
$$FL/2 = I\omega^2L/2$$
$$T = 1/\theta \sqrt{F/I}$$
would this be correct?
I came up with this more basic question to solve a slightly harder question so I do not know the answer to the above-stated problem.
Hi
I've been taught that any force not going through the centre of mass will create torque.
Consider a rod of length ##L## and negligible mass, with two balls of mass ##m## attached to its ends. Its centre of mass is at ##\frac{L}{2}##.
I have two questions:
1) If a force ##F## is applied to...
I have had a thought experiment in my head for a while now and I am unable to find clear enough examples/info that deal with similar issues, to solve it on my own. This is why I hope that someone in this forum can at least point me towards a solution or provide hints as to where should I be...
Basically, I want to know if my assumptions and workings are correct.
This is how I see this situation.
First, I'm viewing this body as a series of disconnected points, like I have in this animation I made, modeling purely rolling motion. Modeling the body like that worked in that case, and...
Lets say we have a system of two point particles (1. and 2.) which are rotating around an axis. What is written next in my physics course book is: The torque of a 2.body on the 1. body is M21=r1xF21 and the torque of the 1.body on the 2.body is M12=r2xF12. Understandable.
But how? There is no...
Homework Statement
Hello! I have 2 bodies initially at rest, of equal masses with the distance between them a and coordinates ##(a cos(\theta),a sin(\theta))## and ##(-a cos(\theta),-a sin(\theta))##. If we denote ##a_x## and ##a_y## the horizontal and vertical distance between them they...
1. The problem statement:
Consider a solid sphere and a hollow sphere, of equal mass M and equal radius R ,at rest on top of an incline . If there is no slipping which will reach the bottom faster.
2. Homework Equations :
acm = Fext/M (cm= centre of mass)
angular acceleration= torqueext/ I ( I...
Can someone either derive or point me to a derivation of Møller's formula for the relativistic minimum radius of a rotating body? I've been searching for about an hour and it's driving me crazy!
The only "minimum radius" equation I've seen imposes the speed limit c on a classical rotating body...
Is shown like this in my book:
Consider a rotating body with an angular acceleration α. There must be a tangential force component if it is rotating:
For a general point on the body we can write:
Ftan = mi * ai = mi * ri * α (1)
Multiply by ri and sum up you...
Starting at BB everything moves outwards with linear momentum so unless the BB event was rotating where does the angular momentum come from, the Earth rotates, it orbits the sun, the galaxy is rotating and the sun orbiting within it. So it seems that angular momentum is the norm for bodies...
Only rotating bodies have angular momentum?
Is this statement false?
I had read it somewhere that it is false that only rotating bodies have angular momentum,
angular momentum = moment of inertia * angular velocity.
Both deal with rotation. so how is the above statement false?
Suppose I have a disk that is 100,000 km in diameter. I attempt to rotate it at 1 revolution per second.
Am I unsuccessful because the material on the outside edge would have to travel faster then light or am I successful because length contraction at the outside edge reduces the...
Homework Statement
A car turns a corner with a radius of curvature of 11.1 m while braking to reduce its speed. If the brakes generate an angular deceleration of 0.5 rad/s2 what is the magnitude of the acceleration of the car half way through the corner when the car's linear speed is 9.6 m/s...
Homework Statement
Ok, when talking about rotating bodies, we deal with the following accelerations - please correct me if I am wrong:
A radial acceleration (a.k.a. the centripetal-acceleration): w^2*r or v^2/r.
An angular acceleration given by dw/dt.
A tangential acceleration given...
If there are two rigid bodies rotating, (known I) how can you compare their rotation?
Example:
If the object of moment of inertia I is spining at x rad/sec, and its I is changed to i, what is the new speed?
im supposed to show why angular momentum is conserved in a rotating body with no external torques or forces acting on it. i know to use the I_1*w_1=I_2*w_2 where I is the moment of inertia of the object in motion and w is the angular speed. My qu estiosn are:
which equation for Inertia...