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The total torque about some axis is defined as: $\vec{\tau}_\text{tot}=\Sigma \left(\vec{r}_i \times{}\vec{f}_i\right) $ If you change to a parallel axis located $\vec{r}$ away from the first one on the plane of the forces, the new torque will be: $$\vec{\tau}_\text{tot}'=\Sigma \left[(\vec{r}_i+\vec{r}) \times{}\vec{f}_i\right] =\vec{\tau}_\text{tot}+\vec{...


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For the first figure: You are misinterpreting the second law, it only says what happens to an object that is subject to a net force. In this case, if the impact force is larger than the friction, the object will accelerate. The second law doesn't say what happens to the object that produces the force. Now, the third law does, which means that the actuator ...


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The question answered by @SatwikPasani is related but not quite a duplicate. The apparent paradox is resolved by realising that using a frame of reference relative to the sphere which is accelerating down the slope is a non-inertial frame of reference. If there is friction and the no slipping condition is satisfied then the frame of reference attached to ...


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In such a hypothetical situation in which there is no friction between the sphere and plane, there can be no tangential force acting on the sphere, and hence no torque. The only force acting on the sphere would therefore be its weight, and the component of that force acting perpendicularly to the plane would be responsible for its translation down the plane, ...


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The force is not magnified, is the torque that is transmitted; and is not an "amplification effect" of the interaction between atoms. The only role the interactions between atoms play is to hold the lever together. And as long as the forces involved using the lever, are smaller than the internally bounding forces of the lever, it will resist the strain and ...


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If you accept that no external work was done, then if there is a change in the state of a system through which the kinetic energy changed, there must be a corresponding change in potential energy. The key to understanding the (rather poorly narrated) video is that the lecturer implies (at T=2:30) that $\Delta E=0$ from which it follows that $\Delta KE= - \...


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Potential energy change of mass $m$ is equal to kinetic energy change of system ($m$ and $M$) plus wasted energy due to friction between spool and axle. $$mgy=\frac 12mv^2+\frac 12I\omega^2+W_f\tag 1$$ $\omega=\large{\frac{v^2}R}$ As the tension force of the string is constant, then the net force acting on mass $m$ will be constant ($F_{\textrm{net}}=mg-T$)....


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They ask you for the angular acceleration $\alpha$, not the linear acceleration. I could not understand what you did, but you know that torque $\tau=I \alpha$, to find $\alpha$ only divide the torque you have by the moment of inertia $I=mL^2/12$ which corresponds to the moment of inertia of a rod around its center of mass.



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