Yo-Yo Mechanics
A yo-yo is a solid disk (moment of inertia I = ½MR²) unrolling from an axle of radius r. The tension T in the string provides a net upward force and a torque. Newton's 2nd law gives the downward acceleration:
a = g / (1 + I / (Mr²)) = g / (1 + R²/(2r²))
Because R ≫ r, a ≪ g — the yo-yo falls slowly. On the way down, gravitational PE splits into translational KE (½Mv²) and rotational KE (½Iω²) in the fixed ratio R²:r².
A yo-yo is a solid disk (moment of inertia I = ½MR²) unrolling from an axle of radius r. The tension T in the string provides a net upward force and a torque. Newton's 2nd law gives the downward acceleration:
a = g / (1 + I / (Mr²)) = g / (1 + R²/(2r²))
Because R ≫ r, a ≪ g — the yo-yo falls slowly. On the way down, gravitational PE splits into translational KE (½Mv²) and rotational KE (½Iω²) in the fixed ratio R²:r².