System of Particles and Rotational Motion

Topics in this chapter

• Center Of Mass Systems
• Moment Of Inertia And Mass Distribution
• Torque And Rotational Equilibrium
• Angular Momentum And Collisions
• Rolling Motion And Friction
• Rotational Dynamics And Energy

Cheat sheet

Practice questions

1. Question 1Q-E9B5AD

   The center of mass of a system of two particles of masses $m_1$ and $m_2$ is at the origin. If mass $m_1$ is moved by a distance $\vec{d}$ towards the origin, by what distance must mass $m_2$ be moved so that the center of mass remains unchanged?

   1. A.$(m_1/m_2)\vec{d}$ away from the origin
   2. B.$(m_1/m_2)\vec{d}$ towards the origin
   3. C.$(m_2/m_1)\vec{d}$ away from the origin
   4. D.zero
   See the answer and solution
2. Question 2Q-56588F

   A thin uniform circular ring of mass $M$ and radius $R$ is rolling without slipping on a horizontal surface with a linear velocity $v$. The total kinetic energy of the ring is:

   1. A.$\frac{1}{2} Mv^2$
   2. B.$Mv^2$
   3. C.$\frac{3}{2} Mv^2$
   4. D.$2 Mv^2$
   See the answer and solution
3. Question 3Q-A196E0

   A solid sphere, a hollow sphere, a solid cylinder, and a hollow cylinder of the same mass and radius are allowed to roll down an inclined plane from rest at the same height simultaneously. Which of them reaches the bottom of the incline first?

   1. A.Solid sphere
   2. B.Hollow sphere
   3. C.Solid cylinder
   4. D.Hollow cylinder
   See the answer and solution
4. Question 4Q-0AD358

   A uniform rod of length $L$ and mass $M$ is pivoted freely at one end and hangs vertically. It is displaced slightly and released. The angular velocity of the rod when it passes through the bottom-most position is:

   1. A.$\sqrt{\frac{3g}{L}}$
   2. B.$\sqrt{\frac{6g}{L}}$
   3. C.$\sqrt{\frac{2g}{3L}}$
   4. D.$\sqrt{\frac{g}{L}}$
   See the answer and solution
5. Question 5Q-79503A

   A ballet dancer spins with angular velocity $\omega_0$ on a frictionless turntable with her arms outstretched. If she folds her arms such that her moment of inertia decreases to $75\text{ \%}$ of its initial value, her new angular velocity becomes:

   1. A.$0.75 \omega_0$
   2. B.$1.33 \omega_0$
   3. C.$1.50 \omega_0$
   4. D.$2.00 \omega_0$
   See the answer and solution