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<title>ReadingGuide_Ch11_Solution</title>
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<body>
<p><strong>Chapter 11: Angular Momentum</strong></p>
<p></p>
<p></p>
<br></br>
<p><strong>Introduction:</strong></p>
<br></br>
<p></p>
<p>-What is rotational counterpart of linear momentum? <span id="ans">Angular
momentum.</span></p>
<p>-Why would the helicopter in Fig. (11.1) want to rotate in opposite sense to
the blades ? How is it prevented? <span id="ans">To conserve angular momentum.
Counter thrust from tail rotors.</span></p>
<p></p>
<p></p>
<br></br>
<p><strong>11.1 Rolling Motion:</strong></p>
<br></br>
<p></p>
<p>-What is rolling motion? Give examples. <span id="ans">Combination of
rotational and translational motion. Eg. wheels moving on car along highway,
wheels on a ploane landing on runway.</span></p>
<p>-What kind of friction is there between the tires and road surface and
why?<span id="ans">Static. The bottom of the wheel is at rest with respect to
the ground.</span></p>
<p>-Look at how forces are set up and described in the Fig. (11.3) to set up
relation between the linear variables of velocity and acceleration of center of
mass of the wheel in terms of their rotational counterparts.</p>
<p>-What is the required condition for a wheel to roll without slipping? <span
id="ans">frictional force is lesser or equal to product of the coefficient of
friction and normal force.</span></p>
<p>-What is the expression for velocity of center of mass for the wheel
rotating without slipping? <span id="ans">radius times the angular velocity.
Equation (11.1).</span></p>
<p>-What is the expression for acceleration of center of mass for the wheel
rotating without slipping? <span id="ans">radius times angular acceleration.
Equation (11.2).</span></p>
<p>-How can the distance travelled by wheel rotating without slipping is
related to angular variables?<span id="ans">Radius times Angle swept. Equation
(11.3)</span></p>
<p>-Look how the arc length is mapped onto the surface as the wheel rools on
the surface in the Fig. (11.4) .</p>
<p>-Look at Example 11.1 (ROLLING DOWN AN INCLINED PLANE). Look how the
co-ordinate system is choosen, how the gravitatinal force is resolved into
components and how the Newton's law in X- and Y- direction are used to obtain
the relation of accleration and condition for not to slip is obtained for a
solid cylinder.</p>
<p>-What is the expression for acceleration of an object rolling without
slipping? <span id="ans">Eqn. (11.4)</span></p>
<p>-Which acceleration is greater, rolling without slipping or slipping without
rolling?<span id="ans">slipping without rolling.</span></p>
<p><ins>-What kind of friction is there when the wheel is slipping? <span
id="ans">Kinetic.</span></ins></p>
<p>-Example 11.2 "Rolling Down an Inclined Plane with Slipping" : Look how the
co-ordinates are set, how the components are resolved and the Newton's 2nd law
of translational and rotational motion are used to calculate the linear and
rotational acceleration for a solid cylinder rolling down in a inclined plane
with slipping.</p>
<p>-Is total mechanical energy is conserved in both rolling with slipping and
rolling without slipping? <span id="ans">No, it is only conserved in rolling
without slipping.</span></p>
<p>-Why the rolling without slipping conserves energy? <span id="ans">Point of
contact with surface is zero.</span></p>
<p>-Example: 11.3 "Curiosity Rover": Look how the conservation of total
mechanical enrgy is used to calculate the velocity of wheel of Curiosity
Rover.</p>
<p></p>
<p></p>
<br></br>
<p><strong>11.2 Angular Momentum:</strong></p>
<br></br>
<p></p>
<p><ins>-Is total angular momentum in universe conserved? <span
id="ans">Yes.</span></ins></p>
<p>-What is angular momentum? What is its unit? <span id="ans">cross product of
position vector and momentum vector. Eq. (11.5). kg.m<sup>2</sup>/s.</span></p>
<p>-Look how is the direction of angular momentum is determined using right
hand rule in Fig. (11.9)</p>
<p><span id="prob">-Note: At the bottom of the page 555 of pdf, the equation
given is a single equation in three steps NOT two different equations. The
perpendicular sign seperates "r " and "p" far apart and it looks like two
different equations.</span></p>
<p>-Does the magnitude of angular momentum depends on the choice of origin?
<span id="ans">Yes.</span></p>
<p>-What is the expression for net torque in terms of angular momentum?<span
id="ans">Time derivative of angular momentum. Eqn. (11.6)</span></p>
<p>-Problem-Solving Strategy: First choose co-ordinate system and then write
down the position and linera momentum vector. Find out the angular momentuma
and its direction using the right hand rule. And, find the net torque.</p>
<p>-Example 11.4: Look how the net toruqe found from two different methods, the
derivative of angular momentum and cross product of lever arm & Force, is
same.</p>
<p>-How is angular momentum of a system of N particles found? <span id="ans">By
adding the individual angular momentums. Eqn. (11.7)</span></p>
<p>-What does the Eqn. (11.8) state? <span id="ans">The rate of change of total
angular momentum is equal to the net external torque acting on the system when
both quantities are measured with respect to a given origin.</span></p>
<p>-Example 11.5: Look how the position and velocity of three particles are
used to find the total angular momentum and net torque.</p>
<p><ins>-What should we consider to develop the angular momentum of a rigid
body? <span id="ans">A rigid body made up of small mass
segments.</span></ins></p>
<p>-Which component of angular momentum of all the small mass segments sum up
to non-zero value in Fig. (11.2) and why? <span id="ans">Components along the
axis of rotation. Another perpenduclar components will be cancelled out due to
the identical mass segments in opposite side.</span></p>
<p>-What is the expression for the magnitude of the angular momentum along the
axis of rotation of a rigid body with angular velocity ω ? <span
id="ans">Eqn. (11.9)</span></p>
<p>-Example 11.6: Look how the individual momentum of inertia of arm, forceps
and rock is used to find the total angular momentum. See how the direction of
the total angular momentum is determined. </p>
<p></p>
<p></p>
<br></br>
<p><strong>11.3 Conservation of Angular Momentum:</strong></p>
<br></br>
<p></p>
<p>-What is the conservation of angular momentum? <span id="ans">The angular
momentum of a systems of particles around a point in a fixed inertial reference
fram is conserved if there is no external torque. Eqn. (11.10).</span></p>
<p>-Look at the Fig. (11.14) how the net torque is zero. Also look how the
decrease in moment of inertia when she pulls in her arm leads to the increase
in spinnig speed.</p>
<p>-What causes to increase in the rotational speed of cloud of our solar
system when it was born?<span id="ans">Gravitational force.</span></p>
<p>-Example 11.8: Look how the conservation of angular momentum and time travel
in tuck are used to find out the number of revolutions of the gymnast.</p>
<p>-Example 11.9: Look how the moment of inertia of system before and after the
bullet imbedded in the disk are calculated. Also, see how the conservation of
angular momentum is used to find the combined angular velocity.</p>
<p></p>
<p></p>
<br></br>
<p><strong>11.4 Precession of a
Gyroscop<strong>e</strong></strong><strong>:</strong></p>
<p></p>
<br></br>
<p>-What is gyroscope? <span id="ans">spinnig disk in which the axis of
rotation is free to assume any orientation. </span></p>
<p>-Why gyroscope is very useful in navigation? <span id="ans">Orientation of
the spin axis remains same when moved from one place to another.</span></p>
<p>-What is the expression of precession velocity of a top rotating about its
axis? <span id="ans">Eqn. (11.12).</span></p>
<p><strong></strong></p>
</body>
</html>