Multiple-Concept Example 10 provides one model for solving this type of problem.

Question

Multiple-Concept Example 10 provides one model for solving this type of problem. Two wheels have the same mass and radius of 4.9 kg and 0.37 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 7.7 s. Find the net external torque that acts on each wheel.

Explanation / Answer

Given Mass of wheel m = 4.9 kg Radius of wheel r = 0.37 m The wheels start from rest and have a constant angular acceleration               = t + ( 1 /2 ) t 2   Angular acceleration of wheel is                 = 2 / t 2                     = 2 ( 14 rad ) / 7.72                   = 3.6363 rad /s 2   . a) Moment of inertia of hoop            I = M r 2 Torque acts on wheel is           = I              = ( M r 2 ) ( )              = ( 4.9 kg ) ( 0.37 m ) 2 ( 3.6363 rad /s 2 )             =   2.4392 kg m 2   ________________________________________________________ b) Moment of inertia of solid disk is           I = ( 1 /2 ) M r 2 Torque acts on wheel is           = I              = ( 1 /2 )( M r 2 ) ( )              =(0.5 ) ( 4.9 kg ) ( 0.37 m ) 2 ( 3.6363 rad /s 2 )             =   1.2196 kg m 2             = I              = ( 1 /2 )( M r 2 ) ( )              =(0.5 ) ( 4.9 kg ) ( 0.37 m ) 2 ( 3.6363 rad /s 2 )             =   1.2196 kg m 2  

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