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Recommends Farcher · 2016-08 · Physics Stack Exchange · on “Applying a force on an object in space (weightless) away from its centre of mass vs at its centre of mass”

I think that you query is about equating the work done by the accelerating force and the gain in kinetic energy of the bar. If the force $F$ is applied at the centre of mass of the bar and the centre of mass moves a distance $x$ then the work done by the force is $Fx$ and this represents the gain in the translational kinetic energy of the bar. If the same force is applied along a line which is not through the centre of mass of the rod and the centre of mass moves by a distance $x$ the work done by the force is larger than $Fx$ because, if the force is to stay in contact with the rod which is rotating about its centre of mass as well as the centre of mass undergoing transnational motion, the

Recommends Diracology · 2017-06 · Physics Stack Exchange · on “For a force to cause translation motion is it necessary to be applied to the center of mass?”

In fact, in a an environment dominated by friction, the answer might not be obvious. To find the answer analytically, recall that a rigid body is particular collection of particles. Let us decompose the force acting on particle $i$ into $\vec F_i^{ext}$ which is due to particles external to the system and $\sum_j\vec F_{ij}$, where $\vec F_{ij}$ is the force on $i$ due to $j$. Hence $$m_i\ddot{\vec r}_i=\vec F_i=\vec F_i^{ext}+\sum_j{\vec F_{ij}}.$$ Sum over all particles, $$\sum_im_i\ddot{\vec r}_i=\sum_i\vec F_i^{ext}+\sum_{ij}{\vec F_{ij}},$$ use the fact that internal forces cancel up (third Newton's law), $\sum_j\vec F_{ij}=0$, and use the definition of the centre of mass vector, $\vec

Recommends An Ignorant Wanderer · 2019-07 · Physics Stack Exchange · on “If an rod is hit at its edge with an impulse I, why would it move with the same velocity as if it were hit at its center?”

In one of his lectures, Walter Lewin gives the example of a rod which is hit with an impulse on its edge. It starts rotating with angular velocity w, and its center of mass moves with velocity v. Assuming ideal conditions, he then continues to explain that where the object is hit does not matter, the center of mass will always move with velocity v given impulse I. In other words, if the rod was hit right at its center of mass with impulse I, it would still move with velocity v without rotating. I thought that was very unintuitive if we think about energy considerations. My gut instinct told me that the one hit at the center would move with a higher velocity. If it is truly the case that the

Recommends Farcher · 2024-12 · Physics Stack Exchange · on “Why does a rod move faster when struck at the center rather than the edge, despite Newton's second law indicating the same acceleration?"”

One word explains why your ideal world analysis disagrees with your real world observation - friction. Ideal world analysis Linear acceleration of centre of mass of the rod is the same irrespective of where the rod is hit. Angular acceleration about centre of mass is greater when the applied force applies a larger torque about the centre of mass, ie force is applied at right angles to the rod and further from the centre of mass. Real world observation Contradicts theory, as explained above, because of the presence of friction and so much so that many think the theoretical analysis is flawed. In some ways this is like the old idea that a force needed to be applied to a cart (or any other obje