What is Moment of iinertia: Definition and 14 Discussions

I am trying to understand how to find the righting moment of an inflatable trapezoid with 75-pounds at the top. The object at the top is 10" tall and weighs 75-pounds. The 75-pound weight will be fixed to the top of the inflatable trapezoid. The top and bottom of the trapezoid have rigid...

Angular Momentum and Torque are defined about a point. But Moment of Inertia of a body is defined about an axis. There are equations which connect Angular momentum and Torque with Moment of Inertia. How will this be consistent? When I say that the torque of a force acting on a body about a point...

I have come up with two different approaches, but I'm not sure which one is correct since they give different answers. We use the following equation to get the total moment of inertia. ##I_o## = moment of inertia of disk about O axis + moment of inertia of road about O axis Approach 1...

This was the question (The line below is probably some translation of upper line in different language) For disc it was ma^2/2 For ring it was ma^2 For square lamina it was 2ma^2/3 For rods It was different Please explain Thank You🙏

I first tried to calculate the moment of inertia of the bar. The problem is that I don't understand exactly how are the dimensions of the bar. The fact that it has a width ##a## means that its height is ##a##, or that it has an unknown hight and the width is ##a##, like a parallelepiped? After...

Homework Statement A solid cylinder rolls down an inclined plane because of stiction. How does angular velocity change over time? Given: ##m,R,g,\alpha,\mu## where ##\mu## is the friction coefficient Homework Equations [/B] ##J_{cm} = 1/2 m*r^2## moment of inertia m = mass of the cylinder...

Homework Statement Homework Equations F=ma τ = Iα = rF v=rω, a=rα L = Iω Center of Mass/Moment of intertia equations The Attempt at a Solution [/B] So right now I've tried to model the force acting on the ring as it goes around the peg, but I think centripetal force is involved and I'm not...

i know how to calculate the inersia for the cylinder, than i have to take away the inersia of the rectangel, but i can't find an equation for the inersia for a rectangel with the plane spinning perpendicular to the rotation axis, please help !

Homework Statement a spool of radius R1 and R2 (R2>R1) is kept on hortizontal surface. A force f= 2t N (where t is time ) acts on the inner radius tagentially find the angular momentum of the system about the bottomost point of the spool. Homework Equations v=u+at W=Wi+alpha(t) L=IW+mvrThe...

I am trying to determine if a function I have is working correctly. The function computes the moment of inertia for a polygon. To test the function I created a polygon that has 4 points and represents a square of 4 units by 4 units. The answer I am getting is 32. I believe the answer should be...

Homework Statement How much torque is needed to change the speed of spinning rate of a 3.50 kg sphere with a radius of 7.50 m from 900. rpm to 200. rpm in 3.0 s? [-1924  -1.92 x 103 Nm] Homework Equations t = I * α I = (2/5)mr^2 t = F * r The Attempt at a Solution just can't get a crack at...

Homework Statement As shown in the attached figure, 2 forces ##F_1=3N## and ##F_2=5N## are applied on the rod of mass ##1## kg.The separation between the points of application of the 2 forces is 0.2 m. If the rod undergoes only translational motion, find the length of the rod. Note that...

I have a doubt in my mind regarding moment of inertia.in my textbook a question is somewhat like this The center of a disc of mass 'M' and radius 'R' is at a distance 'd' (here 'd' >'R') from a certain point 'O'.what is the moment of inertia of the disc about an axis perpendicular to the plane...

If a ball rolls in a semicircular track starting from one end of track,( the track is kept vertical) and if radius of ball is r and radius of track is R is this expression correct? (When ball reaches lowest point) ##mg(R-r)=\frac{1}{2}I_0\omega^2 + \frac{1} {2}I\omega_1^2+\frac{1}{2}mv^2## where...