Question

3-axis center of mass FIGURE 8.24

Answer 1

Tippe Top Model : - We considen a sphere with roding R and axially symmetric distributed mass M so that CM is shifted from the geometóc center o along the symmetry anis 3 by a R, where oc&L 1 The vector s is the position of com warto ko and ack (cß - ²) = R (sin of the Coso) 3) is the vector from CM to A. си, о 1 SR Newton's Equations for the TT describe the motion of the CM and notation around the cha - Ms = F-mg², i = axF, 3 = x3 = 1x3, where I is the total force acting on the TT at the point A. Here, The angulos momentum is taken worto CM, L=Io where I = I, (îlk + 2 2 t) + Iz 23 to and we op i sinol + bê + wg3 is the angels The frictional force :- we assume that the force acting acting at the Point A has the form f = g 2 - Man It consists of a normal reaction force and of a friction force of viscous type, where In and pe are non-negative co-offers ents.

quations of motion (1) can then be The orginal written as M = mugava , i = ax (Inê-ruga VA), & - - xã where na s-sz? The way of writing the frictional part of the neaction force, - Man A = M (L, 3,5, S, t) In (A) VA The model for the External force, which we use in &n (1) immediately implies that the energy E = 1 m3 + 2 w .Ltings - 2 27 %8 decreasing monotonically for the rolling and gliding TT. A short calculation using the en(1) gives, E = F. VA = -ugn IVA 12<0. : CM of TT is lifted by 2 Ro during inversion, The potential Energy 18 increased. This means that Kinetic Energy decreases during inversion.