What torque would have to be applied to a rod with a length of #3 m# and a mass of #1 kg# to change its horizontal spin by a frequency of #1 Hz# over #2 s#?

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Answer 1 · 2017-11-22T06:50:14

The torque for the rod rotating about the center is #=2.36Nm#
The torque for the rod rotating about one end is #=9.42Nm#

The torque is the rate of change of angular momentum

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

The mass of the rod is #m=1kg#

The length of the rod is #L=3m#

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

#I=1/12*mL^2#

#=1/12*1*3^2= 0.75 kgm^2#

The rate of change of angular velocity is

#(domega)/dt=(1)/2*2pi#

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

So the torque is #tau=0.75*(pi) Nm=0.75piNm=2.36Nm#

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

#I=1/3*mL^2#

#=1/3*1*3^2=3kgm^2#

So,

The torque is #tau=3*(pi)=3pi=9.42Nm#