What torque would have to be applied to a rod with a length of #4 m# and a mass of #8 kg# to change its horizontal spin by a frequency #9 Hz# over #2 s#?

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Answer 1 · 2018-01-11T14:30:03

The torque for the rod rotating about the center is #=301.6Nm#
The torque for the rod rotating about one end is #=1206.4Nm#

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=8kg#

The length of the rod is #L=4m#

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

#I=1/12*mL^2#

#=1/12*8*4^2= 10.67 kgm^2#

The rate of change of angular velocity is

#(domega)/dt=(9)/2*2pi#

#=(9pi) rads^(-2)#

So the torque is #tau=10.67*(9pi) Nm=301.6Nm#

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

#I=1/3*mL^2#

#=1/3*8*4^2=42.67kgm^2#

So,

The torque is #tau=42.67*(9pi)=504/5pi=1206.4Nm#