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Hi,first time posting here, so please be gentle... I am studying a point mass doing uniform circular motion on a horizontal frictionless table with tension in a string fixed at one end as the center. Everything is clear if center of circle is treated as center of rotation 'O' for the $$\tau = I \alpha$$ dynamics equation. It shows that relative to the center, angular acceleration is 0.
However, if I select an arbitrary point 'S' on the edge of the circle and re-establish the equation, I have a contradiction. From geometry consideration, $$\theta_S = 1/2 \theta_O$$, $$\omega_S = 1/2 \omega_O$$, finally since it's UCM, $$\omega_O$$ is a constant, therefore, $$\alpha_S = 0$$. But when I use the dynamics equation $$\tau_S = I_S \alpha_S$$, the torque term is clearly non-zero $$\tau_S = \vec r \times \vec T$$, therefore $$\alpha_S$$ cannot be zero...
Could someone enlighten me where my thoughts are flawed? Thanks,
However, if I select an arbitrary point 'S' on the edge of the circle and re-establish the equation, I have a contradiction. From geometry consideration, $$\theta_S = 1/2 \theta_O$$, $$\omega_S = 1/2 \omega_O$$, finally since it's UCM, $$\omega_O$$ is a constant, therefore, $$\alpha_S = 0$$. But when I use the dynamics equation $$\tau_S = I_S \alpha_S$$, the torque term is clearly non-zero $$\tau_S = \vec r \times \vec T$$, therefore $$\alpha_S$$ cannot be zero...
Could someone enlighten me where my thoughts are flawed? Thanks,
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