43. A cylinder of radius R = 6.0 cm is resting on a roughhorizontal surface. The

Question

43. A cylinder of radius R = 6.0 cm is resting on a roughhorizontal surface. The coefficient of kinetic friction between the cylinder and the surface is0.30 and the rotational inertia for rotation about the axis is given by MR2/2, where M is itsmass. Initially it is not rotating but its center of mass has a velocity of 7.0 m/s.After 2.0 s the velocity of its center of mass and its angular velocity about its center ofmass, respectively, are: 43. A cylinder of radius R = 6.0 cm is resting on a roughhorizontal surface. The coefficient of kinetic friction between the cylinder and the surface is0.30 and the rotational inertia for rotation about the axis is given by MR2/2, where M is itsmass. Initially it is not rotating but its center of mass has a velocity of 7.0 m/s.After 2.0 s the velocity of its center of mass and its angular velocity about its center ofmass, respectively, are:

Explanation / Answer

the torque acting on the cylinder = I * or F * R = I * or kMg * R = I * or = (kMg * R/I) =(kMg * R/MR^2/2) or = (2kg/R) ---------------(1) k= 0.30,g = 9.8 m/s^2 and R = 6.0 cm = 6.0 *10^-2 m the initial angular velocity of the cylinder wo= (v/R) v = 7.0 m/s the angular velocity about its center of mass after t = 2.0 sis w = wo + t the value of is obtained from equation (1) the velocity of its center of mass V = R * w

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