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I am sorry for drawing up very old and closed posting https://www.physicsforums.com/threads/rolling-friction.150891/
but I saw this question many times and I can not understand why do not people simply use well-known theorem which says that power of the forces which are applied to a rigid body is calculated by formula ##(\boldsymbol F,\boldsymbol v_A)+(\boldsymbol \omega,\boldsymbol M_A)##. Here ##A## is a body fixed point; ##M_A## is a net torque abput the point ##A##; and ##\boldsymbol F## is a net force.
From this formula it is clear that the work of friction is equal to zero
but I saw this question many times and I can not understand why do not people simply use well-known theorem which says that power of the forces which are applied to a rigid body is calculated by formula ##(\boldsymbol F,\boldsymbol v_A)+(\boldsymbol \omega,\boldsymbol M_A)##. Here ##A## is a body fixed point; ##M_A## is a net torque abput the point ##A##; and ##\boldsymbol F## is a net force.
From this formula it is clear that the work of friction is equal to zero