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11.5: Rotational dynamics for a solid object
https://phys.libretexts.org/Courses/Berea_College/Introductory_Physics%3A_Berea_College/11%3A_Rotational_dynamics/11.05%3A_Rotational_dynamics_for_a_solid_object
The moment of inertia of the dumbbell relative to the axis through the center of mass is given by: $\begin{aligned} I = \sum_i m_ir_i^2 = mr^2 +mr^2 = 2mr^2 = \frac{1}{2}mL^2\end{aligned}$ Using New...The moment of inertia of the dumbbell relative to the axis through the center of mass is given by: $\begin{aligned} I = \sum_i m_ir_i^2 = mr^2 +mr^2 = 2mr^2 = \frac{1}{2}mL^2\end{aligned}$ Using Newton’s Second Law for rotational dynamics, we find the angular acceleration to be: $\begin{aligned} \vec\tau^{ext}&= I\vec\alpha\\ LF\hat z&=\frac{1}{2}mL^2\vec\alpha\\ \therefore \vec\alpha &= \frac{2F}{mL}\hat z\end{aligned}$ Because the center of mass is fixed (the sum of the forces is zero), t…

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