Question

Multiple-Concept Example 10 provides one model for solving this type of problem. Two wheels have the same mass and radius of 4.2 kg and 0.52 m, respectively. One has (a) the shape of a hoop and the other (b) the shape of a solid disk. The wheels start from rest and have a constant angular acceleration with respect to a rotational axis that is perpendicular to the plane of the wheel at its center. Each turns through an angle of 14 rad in 7.8 s. Find the net external torque that acts on each wheel.

Answer 1

from Question we have mass of wheel = 4.2kg radius of wheel = 0.52m. since we know 0 = W. xt + 1 & ² where 2 = angular acceleration Wo = initial angular Velocity from Question we have 14 - 0 + 1L 7.872 L - 0.4602 rad/s2 since we know moment of inertia of hoop = MR2 about its center = 4.2X (0.52)² = 1.135 kgm2 moment of inertia of solid disk = 1 MR² about its center = 1 x 4.2% (0.522 = 0.567 kg/m2 Since we know Torquet I= moment of inertia x angular acceleration Torque for hoop T - 1.135xo. 4602 = 0.522 N-m Torque for Solid Lisk = 0.567x0.4602=0.261 N-m Hence we found Torque for hoop= 0.522 Nm and for solid Lisk = 0.26 1N-m.