The question was:
I will also include the solution:
So, what is the justification of the first formula [ω=√(C/I)]? I know how to derive simple harmonic equations, this one as I guess is probably similar? But I cannot connect as to how C is used exactly.
And the second formula [ω'=ωβ], I...
When the lamina rotates about A, FA must act on B (because it is the farthest away) perpendicular to AB (so that all of FA contributes to rotation).
Same argument is valid for rotation of lamina about B as well.
Having noted that, I tried two approaches:
Approach 1-
If I assume that the...
The formula for moment of inertia is:
I=mr^2
A common derivation for this is:
1. F=ma
2. τ=rma
3. τ=rmrα = r^2 mα
This is a rotational version of Newton’s second law, where torque replaces force, moment of inertia replaces mass, and angular acceleration replaces tangential acceleration...
Apologies if I make anyone frustrated.
To start, I've only had up to Calculus II so far but I was curious how to use and evaluate integrals used for moment of inertia. I know that the moment of inertia is basically an object's resistance to rotation, and is the rotational analog of mass. I know...
Hi,
I previously posted about the statically indeterminate truck problem. Thank you to everyone who helped me. However, I now realised that isn't the problem I need to solve. I need to know the force of the linear actuators to lift the rear tyres off the ground.
Since the tyres will be...
Hello, I am a computer science major and Ex-Biology grad student, my knowledge in physics is humble, but I got a little curious when my professor derived the expressions of moment of inertia for different objects.
The moment of Inertia of a thin disk is 1/2MR2, but it is the same as the moment...
Hello my dear physicists,
I'm trying to model the varied generated (needed)Torque to rotate a washing machine Drum during a Washing Process
so i assumed that the Model has as Input the target vilocity and as an Output the new needed torque to rotate the Drum(to be as a input for the motor...
I use the moment of inertia I = 1/12ml2 for an axis perpendicular and passing through the center of mass of a rod.
In a cube built out of 12 rods I have 8 rods at a perpendicular distance l/2 from the axis through the midpoint of a cube. These 8 rods contribute the moment of inertia I1 =...
Hello, I'm new here so apologies if this is in the wrong place! I was wondering, hypothetically, what sort of canned food would roll the fastest (assuming the ramp remained constant and the can couldn't be altered)?
I've been looking this up and I know a solid can would roll faster than an...
Homework Statement: So i need to find equations to help me with a bifiler suspension experiment in which i will use a rectangular drop bar as the oscillating object, also any help with the method of this experiment would be greatly appreciated. The end goal is to find the moment of inertia...
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...