Physics
Rotational and Circular Motion
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#89 For a rigid body rolling without slipping, total kinetic energy equals:
A) $I\omega$
B) $\tfrac12 mv^{2}$
C) $\tfrac12 mv^{2}+\tfrac12 I\omega^{2}$
D) $\tfrac12 I\omega^{2}$
#90 A mass $m=2\,\text{kg}$ moves in a circle of radius $r=5\,\text{m}$ with speed $v=10\,\text{m s}^{-1}$. The required centripetal force is:
A) $\dfrac{v}{mr}$
B) $\dfrac{r}{mv^{2}}$
C) $\dfrac{mv^2}{r}$
D) $mvr$
#91 Work done by a constant torque $\tau$ through angle $\theta$ is:
A) $W=\tau/\theta$
B) $W=\tau\,\theta$
C) $W=I\omega$
D) $W=\alpha\theta$
#92 A mass $m=2\,\text{kg}$ moves in a circle of radius $r=5\,\text{m}$ with speed $v=4\,\text{m s}^{-1}$. The required centripetal force is:
A) $mvr$
B) $\dfrac{mv^2}{r}$
C) $\dfrac{v}{mr}$
D) $\dfrac{r}{mv^{2}}$
#93 On a frictionless banked curve of radius $r$ and bank angle $\phi$, the ideal speed is:
A) $v=\sqrt{g/\tan\phi}$
B) $v=\sqrt{gr\tan\phi}$
C) $v=rg\phi$
D) $v=\sqrt{rg\tan\phi}$
#94 For a rigid body rolling without slipping, total kinetic energy equals:
A) $\tfrac12 I\omega^{2}$
B) $I\omega$
C) $\tfrac12 mv^{2}+\tfrac12 I\omega^{2}$
D) $\tfrac12 mv^{2}$
#95 On a frictionless banked curve of radius $r$ and bank angle $\phi$, the ideal speed is:
A) $v=\sqrt{g/\tan\phi}$
B) $v=rg\phi$
C) $v=\sqrt{gr\tan\phi}$
D) $v=\sqrt{rg\tan\phi}$
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