The sizes and shapes of the bodies under consideration do not significantly affect the solutions of the problems. What does this statement imply?
Added by Juan B.
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The statement suggests that the physical characteristics (sizes and shapes) of the bodies being analyzed are not crucial to the outcomes of the problems being studied. Show more…
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Distances between points in a plane do not change when a coordinate system is rotated. In other words, the magnitude of a vector is invariant under rotations of the coordinate system. Suppose a coordinate system S is rotated about its origin by angle $\varphi$ to become a new coordinate system $\mathrm{S}^{\prime},$ as shown in the following figure. $\mathrm{A}$ point in a plane has coordinates $(x, y)$ in $S$ and coordinates $\left(x^{\prime}, y^{\prime}\right)$ in $\mathrm{S}^{\prime}$ (a) Show that, during the transformation of rotation, the coordinates in $S^{\prime}$ are expressed in terms of the coordinates in S by the following relations: $\left\{\begin{array}{l}x^{\prime}=x \cos \varphi+y \sin \varphi \\ y^{\prime}=-x \sin \varphi+y \cos \varphi\end{array}\right.$ (b) Show that the distance of point $P$ to the origin is invariant under rotations of the coordinate system. Here, you have to show that $\sqrt{x^{2}+y^{2}}=\sqrt{x^{2}+y^{2}}$ (c) Show that the distance between points $P$ and $Q$ is invariant under rotations of the coordinate system. Here, you have to show that $$\sqrt{\left(x_{P}-x_{Q}\right)^{2}+\left(y_{P}-y_{Q}\right)^{2}}=\sqrt{\left(x_{P}^{\prime}-x^{\prime} \rho\right)^{2}+\left(y_{P}^{\prime}-y^{\prime}_{Q}\right)^{2}}$$
A rigid body is defined as a system consisting of a large number of point masses, called particles, such that the distance between the pairs of point masses remains constant even when the body is in motion or under the action of external forces. This is an idealized definition of a rigid body because: A. There is no such thing as true point masses or particles. B. No body of any physical size is strictly rigid because it becomes deformed under the action of applied forces. C. Any object of any physical size is strictly rigid because it is made up of true point masses or particles. Only A and B are correct. Only A and C are correct. Only B and C are correct.
Adi S.
Translational motion of the rigid body is defined as one in which any line, say PQ, remains parallel to a fixed direction. Let $\overline{\mathrm{R}}_{\mathrm{A}}, \overline{\mathrm{R}}_{\mathrm{B}}, \overline{\mathrm{R}}_{\mathrm{p}}, \ldots \overline{\mathrm{v}}_{\mathrm{A}}, \overline{\mathrm{v}}_{\mathrm{B}}, \overline{\mathrm{v}}_{\mathrm{p}} \ldots$ and $\overline{\mathrm{a}}_{\mathrm{A}}, \overline{\mathrm{a}}_{\mathrm{B}}, \overline{\mathrm{a}}_{\mathrm{p}}, .$ denote the position vectors, velocity vectors and acceleration vectors of $\mathrm{A}, \mathrm{B}, \mathrm{P} . . .$ with respect to $\mathrm{O}$. Then, for translational motion. (a) $\overline{\mathrm{R}}_{\mathrm{p}}-\overline{\mathrm{R}}_{\mathrm{A}}$ must be a constant vector (b) $\overline{\mathrm{v}}_{\mathrm{A}}=\overline{\mathrm{v}}_{\mathrm{B}}=\overline{\mathrm{v}}_{\mathrm{p}}=\ldots$ and $\overline{\mathrm{a}}_{\mathrm{A}}=\overline{\mathrm{a}}_{\mathrm{B}}=\overline{\mathrm{a}}_{\mathrm{p}}=\ldots$ at any instant $\mathrm{t}$. (c) $\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{P}, \ldots$ must move in straight lines that are parallel. (d) All of the above.
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