# Line integral

The line integralint F(r(t)). r'(t) dtis work. In the movie below the force is produced by the leafblower The expression F(r(t)).r'(t) is the power and the integral over time the energy gained. The energy is given by

E = I wwhere w is the angular velocity and I is the moment of inertia of the kid. If we know the power of the blower, the moment of inertia of the kid, then we can compute the angular velocity at time t. The kid should have done that.^{2}/2