Question

1) Define "moment of intertia". What is the formula for the moment of intertia for a point particle? What is the formula for a thin ring rotating around its center? For a flat disk? Explain why the moment of interia is smaller for a disk versus a ring. 2) What is Newton's 2nd law in rotational form? 3) Explain (using plain language) what the parallel axis theorem allows us to do. 4) Three particles lie in the x-y plane: A 100 gram particle lies at point (1,1), a 200 gram particle lies at point (-2,0), and a 300 gram particle lies at point (0,-3). All distances are measured in meters. What is the moment of inertia for this system rotating in the x-y plane around the origin?

Answer 1

4) I Moment of inertia: this is a quatity that describes the resistance of a body to translational motion. it must be specitied with a chosen axis of rotation. when we consider a point mass, the moment of inertia becomes the mass of the point times the square of the perpendicular distance between the mass and the rotational axis. this can be the base of calculating the moment of inertia for various bodies as they would be a combination of points. so morment of inertia for a point mass- : ช where m= mass of the point and the perpendicular distance from the axis is "r" the moment of inertia for a thin ring about an axis through its center is given by 2 where M- mass of the ring R- perpendicular distance from the axis the moment of inertia for a flat disk is given by 2 The difference of mass and the moments of inertia calculated about the x and y axis are the reason tor the moment of inertia of the disk being lesser than that of a thin ring. Because of the lesser mass of the ring, it tends to have higher rorational inertia. 2. Newton's second law in rotational form states that the angular acceleration is directly proportional to the net torque and is inversely proportional to the moment of inertia of the body 3. parallel axis thorem allows us to determine the mass moment of inertia or the second moment of area of a rigid body about any axis, given the body's moment of inertia about a parallel axis through the center of gravity of the body and perpendicular distance between them The parallel axis theorem states that if a body is made to rotate about an axis parallel to the axis through the center of mass displaced by a distance, the moment of inertia with respect to the new axis is related to moment of inertia about the center of mass as follows: 2 moment of inertia about the new parallel axis moment of inertia about the axis through center of mass mass of the body distance between the axes T m c en00 200 + 800 + 2400-3700