Angular Impulse/Momentum for Rigid Bodies in a Plane

 

 

Example:   The figure below shows a hollow drum of weight, W, subjected to a constant torque,

M k, and a force, F i lb, via a wrapped cord.  The diameter of the drum is D and its radius of gyration

is  kZO.  The drum rotates freely about a fixed horizontal axis, O, with an initial angular velocity,

 ˗ ωO k rad/sec.   Find the time, t*,  that it takes the drum to reach an angular velocity  ωf  k  rad/sec.

 

Applicable data:     W = 64.4 lb,  D = 6.0 ft, kZO = 24 inches,  M = 80 k lb ft,  F = 10 lb

ωO =  ˗ 50 rad/sec,  ωf  =  50 rad/sec. 

 

 

                                  

 

                                                                                                                                                                                             Strategy: Apply the Principle of Angular Impulse and Momentum

                             (angular impulse = change in angular momentum)

               t*

               ʃ (∑ M(t) dt k  =  IZZO (ωf ˗ ωi ) k

             0

 

 

         (  M ˗ FR ) t*  =  (W/g) kZO2 (ωf ˗ ωO )

 

                                   t*  = [ (W/g) kZO2 (ωf ˗ ωO )] / ( M ˗ FR )

 

Note:  Expression for  t*  checks dimensionally.

 

 

                        t*  = [ (64.3/32.2)( 22) (50 ˗ (˗ 50) )] / [ 80 ˗ (10)(3) ]  =  16 seconds  (result)

 

Click here for another example.

 

 

 

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