$2.4.1.$ Balls of mass $m$, each connected by a thread, move in a circle with a constant velocity $v$. The kinetic energy of each ball, equal to $\frac{mv^2}{2}$, does not change. If we switch to a reference frame in which the center of the thread moves in a straight line in the plane of rotation at a speed $,$ the energy of each of the balls changes from zero to $4 \frac{mv^2}{2}$. What causes this energy change? Does the total kinetic energy change in the specified reference frame?
In the initial, stationary frame of reference, the energy of the system is $$E_{k1} = 2\frac{mv^2}{2}$$ Velocity of the system $$v_s = \frac{mv+mv}{2m} = v$$ In the inertial frame of reference of the system moving with velocity $\vec{v}$ $$E_{k2} = 0 +\frac{m(2v)^2}{2}=4 \frac{mv^2}{2}$$ To go to the inertial frame of reference, it is necessary to give the system of total mass $2m$ a velocity $v$ $$\Delta E_k = \frac{2mv^2}{2}$$ Thus, the law of conservation of energy is fulfilled and there is no change in total kinetic energy in the reference frame $$\boxed{E_{k2} = E_{k1} + \Delta E_k}$$
In a moving frame of reference, the tension force does work. No.
Almaskhan Arsen