Inertia Definition and 1000 Threads

Inertia moment of a thin square side 2b about the center of mass... I put the coordinates in the center of the square and came to: Integral of (x²+y²)dm = Integral of (x²+y²)*(dxdy)M But, the interval of the integral is [0,b] to x and y And, since this consider just the integral of one...

Hey guys. Im trying to figure out how to calculate the moment of inertia from a homogeneous ball based on a series of accelerations. The ball is released from the top of an incline plane (3.33 deg) and with a motion sensor, 5 values of acceleration where captured . Together with the radius and...

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...

Why we divide the equation dI = dm*r^2 by two when we calcule the moment of inertia of a cone relative to its symmetry axis?

I know that a hoop should have a higher rotational inertia than a solid disk because its mass is distributed further from the axis of rotation. What I don't understand is how a disk of the same mass and radius can have a higher rotational inertia. If the objects roll freely their axes of...

If I take the three masses individually and try to calculate the moment of inertia of the system separately then I=(m*0²)+(m*(l/2)²)+(m*l²) =ml²/4 +ml²=(5/4)ml² But If I try to calculate Moment of Inertia of the system using its Centre of mass then As centre of mass is located at the the...

Given:Thin, homogeneous, curved rod with radius of curvature 𝑅 See figure to the down. Find: The moment of inertia 𝐼𝑥′𝑥 ′ with respect to 𝑥′- the axis passing through the center of mass (point 𝐺). Can someone who can help me ?

So in the above image, I intend to find the moment of inertia of that black rotating object which rotates due to torque which is provided by placing mass on the pulley. But the thing is that this rotating object is kind of like a ball bearing kind of system and even for a small torque it starts...

I tried to find the moment of inertia of 2 rods connected at the corners by adding up their moments of inertia: \frac{1}{3}(\frac{M}{4})a^2 + \frac{1}{3}(\frac{M}{4})a^2 = \frac{1}{6}Ma^2 I then tried to solve for the moment of inertia at the center of mass of the 2 rods using the parallel...

Hi all. I just watched a great video on gravity wave 'telescopes'. So i have been wondering if any of my intuitive hunches are right about gravity waves. Accelerated masses generate gravity waves that dissipate energy.. So let's say i turn my rocket ship engine on while sitting in deep...

Hi, A well-known part of the formula for calculating the deflection stress is ##I_z=\int \int r^2 dA## Usually a moment of inertia is something related to how difficult is to move an object. In this case is understandable but i don't understand the meaning of the double integral. Using ##r^4##...

So, this may be a really stupid question, and I strongly feel as though I'm missing something here. How can it be that objects of different masses have the exact same acceleration when mass is in fact resistance to acceleration? And then, if in (a vaccum) I throw upwards M and m ( a bigger and a...

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...

Since the problem gave me the kinetic energy and inertia of the iron block, I could plug it into the equation K = 1/2 mv^2 to get the final velocity, I got sqrt(30) for the block's final velocity. From there, I don't really know where to go, I could plug it into the equation above, but ΔE int is...

When I solved the problem using the conservation of angular momentum, I have got the correct result (ω = 0.006 rad/s). However, when I tried to find the answer using the conservation of energy the result was incorrect and I do not understand why.

I have to find the inertia tensor of these rods and I don't have the concept that clear... I mean, I know the formulas like: ##I_{xx}=\int y^2 + z^2 dm## ##I_{xy}=\int xy dm## But I don't know what ##x, y, z, dm## stand for. In other words, I don't know what I should replace in the formula...

Can someone guide me on how to approach this question? I tried to draw a quick diagram of what I think is happening here Does the question imply that this object is undergoing horizontal circular motion in the shape of a conical pendulum? Thanks for any help!

Here is the problem that I am finding difficult to answer I had tried using conservation of energy to do this question Where I know that the gravitational potential energy at the top of the slope equals to the sum of both the linear and rotational kinetic energy at the bottom of the slope...

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 =...

inertia of center = [(1/12) m*L^2 + m(L/2)^2]*4 inertia of center = (4m*L^2)/ 3 inertia around pin = (4m*L^2)/ 3 + 4m(L/ 2^(1/2) )^2 inertia around pin = (10m*L^2)/ 3 inertia around pin = (10*0.1*1^2)/ 3 = 0.33 kg*m^2 d= 1/2^(1/2) = 0.707m (m*g*d/inertia)^1/2 = 2pi/period...

I converted the amount of rotations completed in 5 seconds into radians. 23.4 rot * 2pi = 147 rad I found the angular acceleration of the object in the first 5 seconds it was speeding up. Wf = Wi + at a = 5.881 rad/s^2 I then used the moment of inertia given in the problem to solve for torque. T...

Summary: How to define dimensions of an inertia wheel Firstly, I have been working in aviation industry, making me to involve in the Physics a lot. For the last few weeks, There have been a problem to solve since the manfacturer had not wanted to help us by not sharing information. We have...

Well, I just had this thought earlier, and I want to share it. Here it is. So, we all know about inertia, right? The resistance to acceleration, or change in motion. Well, there is also a concept about derivatives of acceleration, mainly jerk and yank. If you don't know, jerk is said to be the...

What I did: ##\frac{dm}{dA} = \frac{M}{\frac{3\sqrt3 R^2}{2}}## ##dm = \frac{2M}{3\sqrt3 R^2} dA## (1) ##dA=3\sqrt3 rdr## (2) (2) in (1) ##dm = \frac{2M}{3\sqrt3 R^2} 3\sqrt3 rdr## Now in the integral ##I = \int \frac{r^2 2Mrdr}{R^2}## How can I solve the integral interval? I think I...

Homework Statement: Derive the formula for the moment of inertia of a thin spherical shell using spherical coordinates and multiple integrals. Homework Equations: Moment of Intertia is (2MR^2)/3 I = (2MR^2)/3

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...

Hello, I'm slowly getting crazy about this stuff. I'm trying to understand what are thermal inertia/effusivity and information have been incoherent so far. The best example of that is seen on wikipedia where the only mention of thermal inertia is in the article...

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...

Hello, I tried to put it in an equation, but it didn't really work out. In this situation, the car was about the size of a model, and, while not exact, the radius of each wheel couldn't have been more than like a centimeter. Conversely, the ball was like twice the size of the car and had a...

∫ λ(x)=0.2 kg/m + 0.061(x/L)^2 kg/m = 0.2(x) + (0.061/3) (x^3) /(1/L^2) mass of rod = 0.2+ (0.061/3) =0.22 kg inertia of rod through nail = (1/3) (mass) (L)^2 inertia of rod through nail = (1/3) (0.22kg) (1m)^2 = 0.073 kg*m^2 torque magnitude = (53N) (0.5m) = 26.5N*m angular...

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

So to start off, what I will do find the center of mass of each of the rods. So for the top rod, COM is at where y= 0.5 L and COM of the rod at the bottom is at x = 0.5 L. From there, how do I proceed in finding the moment of inertia using parallel axis theorem? Do I simply treat: ##I...

I have the moment of inertia for the core(initial) and full body(final) but my answer for the moment of inertia for the arms(initial) was incorrect. Arms(initial) moment of inertia:(1/12)(6)(1.7^2)=1.445 this is incorrect for some reason Core(initial) moment of inertia: .9558 Full...

https://www.physicsforums.com/attachments/250905 I know the answer, but am not certain how they got Lsin(angle) for R?

I don't know if the value for distance between protons given in the homework is right (##d = 74.14 pm##). Indeed, on the following link : https://brainly.in/question/7147660 , they take a distance equal to ##d = 4\times10^{-10} m##. In all cases, the same formula is applied ...

a) Describe the motion of the spool: it will roll down the plane, rotating counter clockwise. I am confused when setting up equation of torque. If I take center of the spool as pivot, only the tension of thread produces torque but the direction will be clockwise and it makes the spool will move...

I've attempted this question, but the answer seems to be incorrect. Here's my workings: ##I=\int y^2 dm## - standard equation ##dM = \mu * dy * x## - take small slice and find mass of it ##x = 4y-16## - convert equation in terms of x to sub in later ##dM = \mu * dy * 4y-16## ##I=\int y^2 \mu *...

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...

Consider two bodies, A and B, of equal mass set at a short distance. Body A is spinning and body B is at rest. Then, through some kind of electromagnetic device, a strong repulsive force is established between them. Will both be displaced at the same speed?

Homework Statement: How or why does inertia caused the water in a bucket not to fall out when spinning in a vertical circle. Homework Equations: Is the bucket catching the water? I know Inertia is the resistance of any physical object to any change in its velocity.

Homework Statement: How or why does inertia cause the water to stay in the bucket while spinning it vertically? I know inertia is the tendency of an object to remain at rest or in a state of uniform motion, but I am not exactly sure how it causes the water to stay in the bucket while it is...

Problem Statement: Finding the rotational inertia Relevant Equations: I=∑m*r^2 A rigid body of 2 massive globes with homogenous mass distribution and a thin rod is connecting the 2 globes. The globes has radius R1 = 0.18 m and R2 =0.28 m and masses m1=193 kg and m2=726 kg. The thin rod has...

Thanks in advance

Ratio of moment of inertia of a circle and that of a square having same area about their centroidal axis is: Sol: both area and square have same area: ##a^2 = \large\frac{π}{4}\normalsize d^{2}; \large\frac{d}{a} =\large \sqrt\frac{4}{p}## Ratio of moment of inertia of a circle and that of a...

I thought about solving it using components of IAB but since it is a scalar quantity it doesn't seems to be correct . I don't think Perpendicular Axis theorem will work as required Inertia is in the same plane.

While I am reading this article, it says moment of inertia is same at radius of ring and at the center of it. How is that possible?

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 know what the answer is supposed to be, but I don't understand why. Here is my logic as to why I thought a few of these suggestions should be the right answer. "C) Mass is a measure of an object’s ability to resist motion or movement of any kind." Considering F = ma, and that mass is...

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...