Physics
Rotational and Circular Motion
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#129 Choose the correct set of analogies:
A) $F\leftrightarrow I,\ a\leftrightarrow\tau,\ m\leftrightarrow\alpha$
B) $F\leftrightarrow \tau,\ a\leftrightarrow\alpha,\ m\leftrightarrow I$
C) $F\leftrightarrow \omega,\ a\leftrightarrow I,\ m\leftrightarrow\tau$
D) $F\leftrightarrow a,\ m\leftrightarrow\tau,\ I\leftrightarrow\alpha$
#130 A mass $m=0.5\,\text{kg}$ moves in a circle of radius $r=2\,\text{m}$ with speed $v=4\,\text{m s}^{-1}$. The required centripetal force is:
A) $\dfrac{r}{mv^{2}}$
B) $mvr$
C) $\dfrac{mv^2}{r}$
D) $\dfrac{v}{mr}$
#131 On a frictionless banked curve of radius $r$ and bank angle $\phi$, the ideal speed is:
A) $v=rg\phi$
B) $v=\sqrt{rg\tan\phi}$
C) $v=\sqrt{gr\tan\phi}$
D) $v=\sqrt{g/\tan\phi}$
#132 For a rigid body rolling without slipping, total kinetic energy equals:
A) $\tfrac12 mv^{2}$
B) $\tfrac12 I\omega^{2}$
C) $I\omega$
D) $\tfrac12 mv^{2}+\tfrac12 I\omega^{2}$
#133 For a rigid body rolling without slipping, total kinetic energy equals:
A) $\tfrac12 mv^{2}+\tfrac12 I\omega^{2}$
B) $\tfrac12 mv^{2}$
C) $\tfrac12 I\omega^{2}$
D) $I\omega$
#134 A mass $m=1\,\text{kg}$ moves in a circle of radius $r=5\,\text{m}$ with speed $v=2\,\text{m s}^{-1}$. The required centripetal force is:
A) $\dfrac{r}{mv^{2}}$
B) $mvr$
C) $\dfrac{v}{mr}$
D) $\dfrac{mv^2}{r}$
#135 Moment of inertia of a solid disc about the standard axis is:
A) $I=\tfrac23 MR^{2}$
B) $I=ML^{2}$
C) $I=\tfrac12 MR^{2}$
D) $I=\tfrac34 MR^{2}$
#136 Choose the correct set of analogies:
A) $F\leftrightarrow a,\ m\leftrightarrow\tau,\ I\leftrightarrow\alpha$
B) $F\leftrightarrow I,\ a\leftrightarrow\tau,\ m\leftrightarrow\alpha$
C) $F\leftrightarrow \omega,\ a\leftrightarrow I,\ m\leftrightarrow\tau$
D) $F\leftrightarrow \tau,\ a\leftrightarrow\alpha,\ m\leftrightarrow I$
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