# Whats wrong in the torque method to get the time period for a semi cylindrical shell? [closed]

Problem is : My all working is shown here : using 1 and 2 i am getting it to be 2pi√2R/g using energy equation it will lead us to correct answer but why the torque method is not working? Here A is the COM and P is the bottom most point about which i calculated torque so as to prevent consideration of (friction for without slipping conditions). C is centre of cylinder shell

## closed as off-topic by John Rennie, Bob D, Aaron Stevens, stafusa, ZeroTheHeroOct 13 at 15:27

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• Is A the center of mass, and $I_\rho$ the mass moment of inertia about it? Please explain your work. – ja72 Oct 11 at 14:52
• Sry sir , didnt mention earlier : Ip is the moment of inertia about bottom most point , and A is the Centre of Mass of cylindrical shell. – Euler142857 Oct 11 at 15:53
• Anyone pls help @aaron stevens – Euler142857 Oct 12 at 2:17
• Hi, homework-like and check-my-work questions are generally considered off-topic here. We intend our questions to be potentially useful to a broader set of users than just the one asking, and prefer conceptual questions. Can you try making a question about some concepts that you'd need to solve this problem? – stafusa Oct 12 at 11:25
• Why do you have two angles, $\varphi$ and $\theta$. The problem has one degree of freedom, the swing angle $\theta$. Express the equations of motion in terms of this angle and solve them to the form $$\ddot{\theta} = -\omega^2 \theta$$ – ja72 Oct 12 at 23:19

$$\tau_{\rm COM} = I_{\rm COM} \ddot{\theta}$$
When it comes to the equations of motion, tracking the center of mass is key because it separates the linear and angular equations, and as a result, the angular equation needs to be about the center of mass. Similarly the linear motion has to be of the center of mass, as in $$F = m \, a_{\rm COM}$$.