Approximately%20how%20much%20torque%20must%20a%20major%20league%20baseball%20player%20exert%20in%20order%20to%20accelerate%20a%20baseball%20bat%20in%20a%20quarter%20of%20a%20circle%20swing%20to%20a%20speed%20at%20its%20tip%20of%2048.0%20m/s%20if%20the%20bat%20is%200.80%20m%20long%20and%20has%20a%20mass%20of%204.1%20kg?

1
Approximately how much torque must a major league
baseball player exert in order to accelerate a
baseball bat in a quarter of a circle swing to a
speed at its tip of 48.0 m/s if the bat is 0.80 m
long and has a mass of 4.1 kg?
Physics 1710Warm-up Quiz

0

1. 1 Nm
2. 10 Nm
3. 100 Nm
4. 1000 Nm

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61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80
2
Physics 1710Chapters 6-10
0

• Solution

t I a I 1/3 mL2 a ?2/(2??) ? v/L t (1/3
mL2 )(v/L)2/(2??) 1/6 m v2 /?? t 1/6 (4.1
kg)(48 m/s)2 /(3.14/2) 1002 Nm
3
Physics 1710Chapters 6-10
0

• Translational vs Rotational Kinematics

Translational ?
Rotary?
x v a vfinalvinitial at xfinalxinitial
vinitialt ½ at2 vfinal 2vinitial 2
2a?x m F F m a

• ? x/R
• ? v/R
• a a/R
• ? final ? initial a t
• ?final ? initial ? initialt ½ at2
• ? final 2 ? initial 2 2 a ? ?
• I ?R2dm
• t R x F
• t Ia

4
Physics 1710Chapters 6-10
0

• Linear vs Rotational Kinematics

Rotary?
Translational ?
p mv F dp/dt Ktrans ½ mv2 Utrans - ? F
dr Etrans Ktrans Utrans

• L R x p
• t dL/dt
• Krot ½ I ? 2
• Urot - ? t d ?
• Erot Krot Urot

??Center of Mass RCM (Smi ri)/ Smi Parallel
Axis Theorem Iparallel ICM MRCM2 Total E
Etrans Erot
5
Physics 1710Chapters 6-10
0

• Which has the greater moment of inertia a ring
  (of mass M, radius R) rotating about its center
  or a similar disk rotating about a point on its
  circumference?

Peer Instruction Time
6
Which has the greater moment of inertia a ring
(of mass M, radius R) rotating about its center
or a similar disk rotating about a point on its
circumference?
Physics 1710Chapters 6-10

0

1. I bigger for ring.
2. I bigger for disk.
3. I the same for each.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
7
Physics 1710Chapters 6-10
0

• Solution

IRing mR2 IDisk IDisk-CM mR2 IDisk ½ mR2
mR2 3/2 mR2 gt Iring
8
Physics 1710Chapters 6-10
0

• 1' Lecture (Review)
• Rotary (circular) motion obeys laws that are
  analogous to those of translational motion.
• Linear Momentum is conserved in absence of
  external forces.
• F d p/dt
• Energy is related to the work done or stored
• Work is the cumulative force times distance
  moved.
• Power is the rate of expenditure of work or
  energy.

9
Physics 1710Chapters 6-10
0

• Circular Motion
• Acceleration
• Centripetal aC - ?2 r a v 2/r, toward
  center
• Tangential aT r d ?/dt

10
Physics 1710Chapters 6-10
0

• Work and Power
• W ? Fd r ? t d ?
• P dW/dt Fv t ?
• Units
• WorkJoule
• PowerWatt Joule/sec

11
Physics 1710Chapters 6-10
0

• Work and Kinetic Energy
• If only change is speed vor rotation rate ?
• SW Kfinal K initial
• Kinetic Energy K
• Ktrans ½ mv2
• Krot ½ I ? 2

12
Physics 1710Chapters 6-10
0

• Work and Potential Energy and Force/Torque
• ?U - SW
• Force and Torque from Potential Energy
• Fx - dU/dx
• Fy - dU/dy
• t - dU/d?
• Gravitational Potential Energy Ug mgy
• Elastic Potential Energy Ue ½ kx2
• Total Mechanical Energy E K U

13
Physics 1710Chapters 6-10
0

• Momentum and Impulse I
• p m v
• In the absence of external forces momentum is
• conserved
• pinitial,1 pinitial,2 pfinal,1 pfinal,2
• pinitial,x,1 pinitial,x,2 pfinal,x,1
  pfinal,x,2
• pinitial,y,1 pinitial,y,2 pfinal,y,1
  pfinal,y,2
• I ?p ?Fdt

14
Physics 1710Chapters 6-10
0

• Momentum and Force (2nd Law od Motion)
• F d p/dt
• t d L/dt

15
Physics 1710Chapters 6-10
0

• Summary (Review)
• Rotary (circular) motion obeys laws that are
  analogous to those of translational motion.
• Linear Momentum is conserved in absence of
  external forces.
• F d p/dt
• Energy is related to the work done or stored
• Work is the cumulative force times distance
  moved.
• Power is the rate of expenditure of work or
  energy.
• Force is the negative of the gradient of the
  potential.