What torque would have to be applied to a rod with a length of #1 m# and a mass of #1 kg# to change its horizontal spin by a frequency of #7 Hz# over #3 s#?

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Answer 1 · 2017-06-08T05:23:09

The torque for the rod rotating about the center is #=1.22Nm#
The torque for the rod rotating about one end is #=4.89Nm#

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

The rate of change of angular velocity is

#(domega)/dt=(7)/3*2pi#

#=(14/3pi) rads^(-2)#

So the torque is #tau=1/12*(14/3pi) Nm=7/18piNm=1.22Nm#

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

#I=1/3*mL^2#

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

So,

The torque is #tau=1/3*(14/3pi)=14/9pi=4.89Nm#