Sunday, 8 September 2019

classical mechanics - Deriving T=Fr=Ialpha for a rigid body


For a single point mass : τ=Ftr=matr=(mr2)α=Iα


For multiple point masses bound together : τi=(mir2i)α=Iα


But how do we go from that to Iα=Ftrapp (for the multiple masses case), where rapp is the point where force is applied? That is saying that the entire sum of torques of individual masses τi is physically equivalent to (i.e. produces the same angular acceleration of the bound rigid object as) a single torque Ftrapp applied to the point rapp. (Or putting it another way, that applying a single force Ftrapp will result in many Ft_i forces on each mass element such that Ft_iri will be equal to Iα.)


Every place I've looked for a derivation just jumps from τi=Iα, to τ=Iα, as if they are the same thing.




No comments:

Post a Comment

Understanding Stagnation point in pitot fluid

What is stagnation point in fluid mechanics. At the open end of the pitot tube the velocity of the fluid becomes zero.But that should result...