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Chapter 10: Dynamics of Rotational Motion
2016 Pearson Education, Inc. Dynamics of Rotational Motion
(Conservation of angular momentum) Goals for Chapter 10 Torque:
angular force
To see how torques cause rotational dynamics (just as linear forces
cause linear accelerations) To examine the combination of
translation and rotation To calculate the work done by a torque To
study angular momentum and its conservation To relate rotational
dynamics and angular momentum To study how torques add a new
variable to equilibrium To see the vector nature of angular
quantities. Rotational Dynamics: I Clicker question The figure
shows two equal-mass blocks suspended by a cord of negligible mass
that runs over a pulley with half the mass of a block. The blocks
are moving with constant velocity. How do the magnitudes of the
forces and exerted by the cord on the two sides of the pulley
compare? a) They are equal. b) FA > FB c) FA < FB Answer: a)
They are equal. 2016 Pearson Education, Inc. Definition of Torque
Figure 10.1
Torque ( ) is defined as the force applied multiplied by the moment
arm. The moment arm is the perpendicular distance from the point of
force application to the pivot point. 2016 Pearson Education, Inc.
A Plumbing Problem to Solve Example 10.1
2016 Pearson Education, Inc. Torque Note: F(rad)has no torque with
respect to O There Is a Sign Convention Figure 10.3
A counterclockwise force is designated as positive (+). A clockwise
force is designated as negative (). 2016 Pearson Education, Inc.
Note: t = F R sinq Note: sign of t Why Do Acrobats Carry Long
Bars?
Refer to the photo caption on the bottom of page 287. 2016 Pearson
Education, Inc. Rotating Cylinders Clicker Question
Relationship of torque and angular acceleration =rotational analog
of Newtons law = Which choice correctly ranks the magnitudes of the
angular accelerations of the three cylinders? A. 3 > 2 > B. 1
> 2 > 1 C. 2 > 1 > D. 1 = 2 = 3 2016 Pearson Education,
Inc. Unwinding a Winch (Again) Example 10.2
2016 Pearson Education, Inc. A Bowling Ball Rotates on a Moving
Axis Example 10.5
2016 Pearson Education, Inc. Work and power in rotational motion
Clicker question The block in the figure slides in a circle on a
nearly frictionless table with a speed v. You hold it by means of a
string passing through a hold in the table. If you raise your hand
so that the radius of the block's circle doubles, the block's final
speed will be 2v. 1/2v. 1/4v. d)v. Answer: b) 1/2. 2016 Pearson
Education, Inc. Angular momentum Angular Momentum Is Conserved
Figure 10.19
The first figure shows the figure skater with a large moment of
inertia. In the second figure, she has made the moment much smaller
by bringing her arms in. Since L is constant, must increase. 2016
Pearson Education, Inc. Conservation of angular momentum
L=r x p |L|=(rp)sin90=(r)(mv) v=r 5 kg Conservation of L Angular
Momentum Figure 10.15
The diver changes rotational velocities by changing body shape. The
total angular momentum is the moment of inertia multiplied by the
angular velocity. 2016 Pearson Education, Inc. Equilibrium
condition for equilibrium
Center of gravity is the turning point A New Equilibrium Condition
Figure 10.24
Now, in addition to , we also must add 2016 Pearson Education, Inc.
Balancing on a Teeter-Totter Figure 10.26
The heavier child must sit closer to balance the torque from the
smaller child. Your torque is =+ 90 Your friend is 3.0 m from the
pivot, and her torque is: = 60 3.0 m . For equilibrium, =0. + =0 +
90 kg 60 kg 3.0 m =0 =. 2016 Pearson Education, Inc. Walking the
plank A fishy wind chime Hanging a farm gate Carrying a box up the
stairs
F How a cars clutch work The clutch disk and the gear disk is
pushed into each other by two forces that do not impart any torque,
what is the final angular velocity when they come together? Problem
10.74 What is the original kinetic energy Ki of disk A? = 1 3 =3
Initially; = and = 1 2 2 Final; = +3 =4 (after coupling together)
Conservation of angular momentum; = = ==4 = 4 Final Kinetic energy;
= 1 2 2 = 4 2 = 1 4 = = 3 4 =2400 (thermal energy developed during
coupling) So, original energy; = 3 42400 =3200 Honda 600RR Who
races this bike? Why can anybody race it, if he just
dares to go fast? The oval track of the Texas World Speedway allows
speeds of 250 mph. Angular Quantities Are Vectors Figure
10.29
The "right-hand rule" gives us a vector's direction. 2016 Pearson
Education, Inc. Vector nature of angular quantities A non rotating
and rotating gyroscope Precesion Angular Velocity
= = = Analogous to = = = = = = rad/s is the weight of the flywheel,
and is the distance from the pivot point of the center of mass of
the flywheel.