2024年10月12日 · The force of static friction, therefore, is such that it balances the linear deceleration and the rotational deceleration - and can thus be calculated. The other side of this phenomena is that objects will roll down a slope with different accelerations depending on their moment of inertia.

2005年1月8日 · I was wondering about the equation for the moment of inertia of a uniform disc rotating about it's central axis. My book tells me that it's 1/2MR^2, but I attempted to arrive at that same equation myself and got MR^2, which is wrong-o.

2011年10月13日 · The moment of inertia is the mass of the object times the mass-weighted average of the squared distance from the axis. Because the ring is hollow, all of its mass has to sit at a distance R from the center; hence, you have <r 2>=R 2 and I = MR 2.

2009年11月17日 · Your equation for moment of inerta of a half cylinder is incorrect as well as your distance used for the parallel axis theorem. Recall that it is from the axis of rotation to the objects centroid. Review your equation and find the half-cylinders centroid.

2004年3月7日 · In summary, the moment of inertia (I) for something is equal to the integral of y^2 over the area A of the shape. If the integration was done correctly, you should get I = \frac {\pi r^4} {4}dA.

2019年6月30日 · In summary, the ratio of moment of inertia of a circle and that of a square having the same area about their centroidal axis is equal to 3/π. This calculation assumes that the centroidal axis is in the plane, and not normal to it.

2011年10月11日 · Homework Statement having some major derp problems. I can't seem to remember how to find moment of inertia about the COM of and object or even finding the COM for that matter. I need it to solve a Euler Lagrange problem Can someone give me an idea on the integrals to use and in what...

2007年11月6日 · In summary, moment of inertia is a measure of an object's resistance to changes in its rotational motion and is calculated by considering the mass and distribution of mass around a specific axis of rotation. For a circle, it can be calculated using the formula I = mr², where I is the moment of inertia, m is the mass, and r is the radius. The units of moment of inertia …

2015年12月16日 · In summary, the conversation discusses an object hanging from a ceiling and its moment of inertia at a point on the ceiling. The mass and length of the rope are also mentioned. The solution involves using the equation I=∫mr^2dr and the parallel axis theorem for objects that are not point masses.

2010年6月15日 · In summary, the problem involves finding the moment of inertia of a modified disk with a circular hole of radius 7.2 cm cut out of it. The moment of inertia is calculated using the equation I = 1/2 MR^2 and the parallel axis theorem is used to take into account the moment of inertia of the hole relative to the origin of the disk.