Why is the gravitational potential energy of the chain's center of mass equal to the total kinetic energy of the disc after it was fully wrapped? My first thought was to write ##E_{0}=(M/2+M)g∗2πR=E_{f}= Ep## (from the chain) ##+Ec## (from the disc). Instead he wrote ## mg \frac{l}{2} ## = ##...
Spinning objects have strange instabilities known as The Dzhanibekov Effect or Tennis Racket Theorem - this video offers an intuitive explanation. Part of th...
Homework Statement: Derive the formula for moment of inertia of a hollow sphere.
Homework Equations: Required answer ##\frac{2MR^2}{3}##
Consider a Hollow sphere.
At an angle ##Θ## with the vertical, consider a circular ring whose moment of inertia is given by ##MR^2##.
The most basic...
I am interested in climate change and thereby interested in tipping points. So for the last few months, I have been investigating the dynamics of a toppling brick. I derived a differential equation of for the motion and wrote a computer program to solve this from initial conditions.
I have more...
My attempt-:I extended the axis and made a triangle by joining other adjacent vertex to the line such that its angles are 15°,75° and 90°.I found the distance between the centre of square and upper vertex of triangle by using law of sines.And then i found out inertia along upper vertex of...
I hope you guys can help me with this problem..
A top in the form of a flat, circular disc spins on a shaft that is inclined at an angle alpha to the vertical.
Now I have to find the moment of inertia I for the disc about its centre on the shaft.
My attempt was building I with spherical...
I write Conservation of Energy:
Potential Energy loss(change):
U = m g ##\Delta##h = m g (R+r) (1-cos##\alpha##)
kinetic Energy gain(change):
K = (##\frac {m v^2} 2## + ##\frac {I \omega^2} 2##) + (##\frac {M v_2^2} 2## + ##\frac {I_2 \omega_2^2} 2##)
U = K
m g (R+r) (1-cos##\alpha##) =...
Calculating moment of inertia and translating it between units, I've become confused.
The example is a mass of 1kg at 2000mm from the pivot. The force is applied at 1000mm from the pivot.
Basics as far as i'm aware:
Moment of inertia = mass * Distance to center of rotation^2
Torque = Moment...
So I first wrote the moment of inertia of the cylinder, since it says that it is thin-walled, I think that its moment of inertia is ##I=\eta mR^2##. After that I wrote the sum of torques, I think that there are three forces that cause torque, the two forces of friction, the one caused by the...
I already solved the first part, but according the my book, the answer isn't quite correct. This is what I did.
Finally, I ended up with ##a=\frac{F(r-R\cos\alpha)}{Rm(\gamma+1)}##. But according to my book, the answer is ##a=\frac{F(\cos\alpha-\frac{r}{R})}{m(1+\gamma)}##, what am I doing...
1. A 20-lbf disc with diameter 18" and thickness of 3" is held static while completely submerged in water. Upon release of a lock, the disc experiences a torque from a torsional spring that causes rotation about its center of mass along the x/y axis (think coin toss, not wheel). If the spring is...
Object to be tilted = 1200mm diameter cylinder
Cylinder height = 2.5 meter
weight of tilting assembly = 1200 kg
Cylinder is on platform which is "L" shaped and tilting point is on that corner of "L" as in attached image.
Shaft diameter on which it is tilted id 63mm
Angular acceleration = 0.05236...
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...
Hey there!
I am working on a project concerning the mathematical modeling of nano-swimmers in a viscous medium. Assuming the nano-swimmers to be cantilever beams, the project involves calculation of moment of inertia of the said nano-swimmers. While calculating the moment of inertia of a simple...
In Chapter 11: Dynamics of Rigid Bodies, in the Classical Dynamics of Particles and Systems book by Thornton and Marion, Fifth Edition, pages 415-418, Section 11.3 - Inertia Tensor, I have three questions regarding the Inertia Tensor:
1.The authors made the following statement: "neither V nor ω...
When a question only asks for the moment of inertia (of say, a T-section), do I have to find the moment of inertia with respect to both the x and the y axis?
1. Homework Statement
The ammonium ion NH4+ has the shape of a regular tetrahedron. The Nitrogen
atom (blue sphere) is at the center of the tetrahedron and the 4 Hydrogen atoms
are located at the vertices at equal distances L from the center (about 1 Å). Denote
the mass of the hydrogen atoms by...
It's been ages since I have done Moments of Inertia of complex objects!! :( Can anyone help?? Say you have an assembly like an airplane and you want to just get the moment of inertia(MOI) of the tail section and you are given the Mass of whole plane,mass of tail section, moment of inertia of...
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...
Im trying to calculate the principals moments of inertia (Ixx Iyy Izz) for the inertia tensor by triple integration using cylindrical coordinates in MATLAB.
% Symbolic variables
syms r z theta R h M; % R (Radius) h(height) M(Mass)
% Ixx
unox = int((z^2+(r*sin(theta))^2)*r,z,r,h); % First...
1. Homework Statement
If two balls, being identical in volume, but different in density (one ball is made of iron, the other of aluminum) roll down from an inclined plane, which will reach the bottom first and which will cover a larger distance after having reached the bottom?
IMPORTANT NOTE...
Is there a method to calculate inertia tensor form principal axes moment of inertia?
Like now we have moment of inertia: (Ix,Iy,Iz)=(20,18,25), and hot to calculate the inertia tensor like
(Ixx,Ixy,Ixz
Iyx,Iyy,Iyz,
Izx,Izy,Izz)?
I have read about this page several times, but still have no idea.
1. Homework Statement
A solid rod of length L and mass M has a pivot through its center and is originally horizontal. Another mass 2M is then attached firmly to one end of the rod, and released. What is the maximum speed of the mass 2M attained thereafter? (Cornell 2009)
2. Homework Equations...
1. Homework Statement
Consider a half disk (of uniform density) with the flat end lying on the x-axis, symmetric about the y-axis (i.e. being cut into two quarters by the y-axis). Calculate the moments of inertia about each of the axes.
2. Homework Equations
$$I_{rr}=\sum_{i}m_ir_i^2$$
3...
1. Homework Statement
A 25kg child is spinning on a merry-go-round of mass 150kg and radius 2m at a constant angular velocity of 1rev/s. The child slowly walks to the center of the merry-go-round. Treat the child as a point mass and the merry-go-round as a uniform solid disk, and neglect...
1. Homework Statement
I am currently working on a physics experiment to confirm the parallel axis theorem. To do this, I have the following setup:
In this experiment I change the distance between the centre of the rotating disc and the central axis. I record the time for 5 complete...
<< Mentor Note -- Two threads on the same subject have been merged >>
I am a junior enrolled in IB Physics at the standard level at my high school. As a part of the curriculum we must perform an Internal Assessment (IA) which involves performing an experiment and performing calculations and it...
1. Homework Statement :
A stationary horizontal platform is free to rotate about its vertical axis. The radius of the platform is R=1.6m and its moment of inertia is 660 kgm^2. A 43 kg boy jumps on the rim of the platform with the velocity 2.2 m/s tangential to the rim. What will be the angular...
1. Homework Statement
Kindly see the screenshot attached below for the question.
2. Homework Equations
I=1/3ML^2
1/12ML^2
3. The Attempt at a Solution
In the solution to this question, the moment of inertia of the hands (when outstretched) is taken to be 1/12ML^2 (combined). I think that it...