# Read about moment of inertia | 144 Discussions | Page 1

1. ### Moment of inertia of a uniform 2D triangular plate

Answer is 37.8 g cm^2 new to latex
2. ### What is a "Torsional Constant"?

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...
3. ### T-Shaped Pendulum

My answer to part A is correct but for Part B I got an incorrect answer of 0.204J. My working out is sent as an attachment. Part A: Part B: Part C:
4. ### Minimum force required to rotate a lamina

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...
5. ### I Moment of inertia where mass and torque are at a different positions

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...
6. ### I How can I calculate the moment of inertia of any object?

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...
7. ### Stabilizer Leg Linear Actuator Force to Jack up a Truck's rear tyres

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...
8. ### B About the Moment of Inertia

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...
9. ### Analytical mathematical modeling of the torque caused by the laundry

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...
10. ### Calculate the moment of inertia of this body

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 =...
11. ### B What sort of can would roll the fastest?

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...
12. ### Torque on a circular disk

moment of inertia= [(1/2)(1.1kg)(0.96)^2+ (1.1kg) (0.75*0.96)^2]= 1.08 kg*m^2 θ=9.8 degrees= 0.17 rad torque= (mass*gravity) * radius * sin(theta) radius= 0.17rad * 0.96m = 0.16m torque= (1.1kg*9.8m/s^2) * 0.16m * sin(0.17rad) = 0.29 N*m torque = inertia * angular acceleration 0.29N*m=...
13. ### Moment of inertia project help- experiment 1: Bifiler Rod

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...
14. ### Moment of inertia of a tire

I=(1/2)(6kg)(0.4^2 + 0.52^2) = 1.29 kg*m^2 initial: 34 mph= 15.2m/s 15.2m/s = (ω) (0.52m) ω= 29.2 rad/s after: 19 mph = 8.5m/s 8.5m/s = ω(0.52m) ω= 16.3 rad/s acceleration = (16.3 rad/s - 29.2 rad/s) / 5s= -2.58 rad/s^2 torque= |-2.58 rad/s^2 |(1.29 kg*m^2 ) = 3.3 N*m I am confused...
15. ### Torque and inertia of a space object

I= 524kg * 6m^2 = 18.86E3kg*m^2 KE=(1/2) (18.86E3kg*m^2) (0.16 rad/s )^2= 241.5 J torque= 0.25* 57N* (6m)=85.5 N*m
16. ### I Rigid body motion - thin disc

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} ## = ##...
17. ### The Bizarre Behavior of Rotating Bodies, Explained

Spinning objects have strange instabilities known as The Dzhanibekov Effect or Tennis Racket Theorem - this video offers an intuitive explanation. Part of th...
18. ### Moment of Inertia of a hollow sphere with Mass 'M' and radius 'R'.

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...
19. ### Rotating pendulum

is this eqn correct
20. ### I The time for a tilted brick to hit the ground

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...
21. ### Moment of inertia of a square along an axis inclined at an angle

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...
22. ### Spinning top's moment of inertia I (disc on shaft )

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...
23. ### Energy Conservation in Angular motion / Moment of Inertia

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##) =...
24. ### Moment of Inertia and units

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...
25. ### Determine the acceleration of the cylinder axis if there is no slip

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...
26. ### Find the acceleration and the work done by a force pulling a spool?

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...
27. ### Rotation of a Submerged Disc

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...
28. ### Torque required to tilt 1200 kg mass?

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...
29. ### Rotation of a Solid Cylinder

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...
30. ### I Moment of inertia of a branched cantilever beam

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...