What torque would have to be applied to a rod with a length of #12 m# and a mass of #7 kg# to change its horizontal spin by a frequency #5 Hz# over #4 s#?

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Answer 1 · 2017-04-12T06:24:01

The torque for the rod rotating about the center is #=659.7Nm#
The torque for the rod rotating about one end is #=2638.9Nm#

The torque is the rate of change of angular momentum

#tau=(dL)/dt=(d(Iomega))/dt=I(domega)/dt#

The moment of inertia of a rod, rotating about the center is

#I=1/12*mL^2#

#=1/12*7*12^2= 84 kgm^2#

The rate of change of angular velocity is

#(domega)/dt=(5)/4*2pi#

#=(5/2pi) rads^(-2)#

So the torque is #tau=84*(5/2pi) Nm=659.7Nm#

The moment of inertia of a rod, rotating about one end is

#I=1/3*mL^2#

#=1/3*7*12^2=336 kgm^2#

So,

The torque is #tau=336*(5/2pi)=2638.9Nm#