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Ch10-1 Angular Position, Displacement, Velocity and Acceleration
Rigid body: every point on the body moves through the same displacement and rotates through the same angle.
Chapter 10: Rotational Kinematics and Energy
CCW +
CT1:A ladybug sits at the outer edge of a merry-go-round, and a gentleman bug sits halfway between her and the axis of rotation. The merry-go-round makes a complete revolution once each second. The gentleman bug’s angular speed is
A. half the ladybug’s.B. the same as the ladybug’s.C. twice the ladybug’s.D. impossible to determine.
Angular Position
Counterclockwise is positive
Radians
= s/r (a dimensionless ratio)
Angular Displacement
Average angular velocity
av = angular displacement / elapsed time
av = /t
Instantaneous angular velocity
= lim /t t 0
Ch2-1 Angular Velocity
Chapter 10: Rotational Kinematics and Energy
CCW +
P10.9 (p.308)
Average angular acceleration
av = angular velocity / elapsed time
av = /t
Instantaneous angular acceleration
= lim /t t 0
Ch2-1 Angular Acceleration
Chapter 10: Rotational Kinematics and Energy
CCW +
Ch2-2 Rotational Kinematics
Chapter 10: Rotational Kinematics and Energy
CCW +
CT2: Which equation is correct for the fifth equation?
A. = 0 +
B. 2 = 02 +
C. 2 = 0 +
D. 2 = 02 + 2
Equations for Constant Acceleration Only
1. v = v0 + at = 0 + t
2. vav = (v0 + v) / 2 av = (0 + ) / 2
3. x = x0 + (v0 + v) t / 2 = 0 + (0 + ) t / 2
4. x = x0 + v0 t + at2/2 = 0 + 0 t + t2/2
5. v2 = v02 + 2a(x – x0) 2 = 0
2 + 2( – 0)
Assuming the initial conditions at t = 0
x = x0 and = 0
v = v0 and = 0
and a and are constant.
1. = 0 + t
2. av = (0 + ) / 2
3. = 0 + (0 + ) t / 2
4. = 0 + 0 t + t2/2
5. 2 = 02 + 2( – 0)
P10.20 (p.309)
P10.22 (p.309)
Ch2-3 Connections Between Linear and Rotational Quantities
s = r
vt = r
at = r acp = v2/r
Chapter 10: Rotational Kinematics and Energy
CT3: A ladybug sits at the outer edge of a merry-go-round, and a gentleman bug sits halfway between her and the axis of rotation. The merry-go-round makes a complete revolution once each second. The gentleman bug’s linear speed is
A. half the ladybug’s.B. the same as the ladybug’s.C. twice the ladybug’s.D. impossible to determine.
P10-29 (p.310)
CT4: P10.29c The force necessary for Jeff’s centripetal acceleration is exerted by
A. gravity.
B. Jeff.
C. the vine.
D. air resistance.
Ch2-4 Rolling Motion
v = r if no slipping
= 0 if no friction
Chapter 10: Rotational Kinematics and Energy
Rolling Without SlippingConstant v and
d = vt2r = vt
(2/t)r = v r = v
recall that r = vt
P10.45 (p.311)
CT5: P10.45b If the radius of the tires had been smaller, the angular acceleration of the tires would be
A. greater.
B. smaller.
C. the same.
Ch2-5 Rotational Kinetic Energy and Moment of Inertia
For N particles: I = miri2 and K = I2/2
Recall for translation K = mv2/2
Both translation and rotation: K = mv2/2 + I2/2
Chapter 10: Rotational Kinematics and Energy
Kinetic Energy of a Rotating Objectof Arbitrary Shape:
Rigid Body of N Particles
Table 10-1aMoments of Inertia for Uniform, Rigid Objects
of Various Shapes and Total Mass M
Table 10-1bMoments of Inertia for
Uniform, Rigid Objects of Various Shapes and
Total Mass M
P10.52 (p.311)
CT6: P10.52b If the speed of the basketball is doubled to 2v, the fraction of rotational kinetic energy will
A. double.
B. halve.
C. stay the same.
Ch2-6 Conservation of Energy
WNC = E with K = mv2/2 + I2/2
Chapter 10: Rotational Kinematics and Energy
Problem 10-60
Before
After
y=0h
vi
vf
i
f
P10.60 (p.311)
CT7: P10.60b If the radius of the bowling ball were increased, the final linear speed would
A. increase.
B. decrease.
C. stay the same.
CT8: In the race between the hoop and solid disk, which will arrive at the base of the incline first?
A. hoop.
B. disk.
C. neither, it will be a tie.
