If you had a uniform bar floating in space and a force was applied to one end perpendicular, how would it translate and rotate and about what point?
if we had a uniform bar floating in space and force F is applied at one end perpendicularly ,
if we applied force F at one end of the rod , then according to newton's second law
FY = m acm { FY = force in Y direction perpendicular to bar }
the force acting only Y direction , so acceleration , acm = F/m .so the rod purely translates as whole and it does not rotates.there is no external torque is acting because the end of the rod accelerating linearly along with the center of mass of bar.
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