Problem 17'71 A semicircular panel of radius r is

1

• Problem 17.71 A semicircular panel of radius r is
• attached with hinges to a circular plate of
  radius r and
• initially held in the vertical position as shown.
  The plate
• and panel are made of the same material and have
  the
• same thickness. Knowing that the entire assembly
  is
• rotating freely with an initial angular velocity
  w0 ,
• determine the angular velocity of the assembly
  after the
• panel has been released and comes to rest against
  the
• plate.

2

• Problem 17.71 A semicircular panel of radius r is
• attached with hinges to a circular plate of
  radius r and
• initially held in the vertical position as shown.
  The plate
• and panel are made of the same material and have
  the
• same thickness. Knowing that the entire assembly
  is
• rotating freely with an initial angular velocity
  w0 ,
• determine the angular velocity of the assembly
  after the
• panel has been released and comes to rest against
  the
• plate.
• I for a plate on edge is (1/4)mr2 for (1/2) plate
  is (1/8)mr2

3

• Problem 17.71 A semicircular panel of radius r is
• attached with hinges to a circular plate of
  radius r and
• initially held in the vertical position as shown.
  The plate
• and panel are made of the same material and have
  the
• same thickness. Knowing that the entire assembly
  is
• rotating freely with an initial angular velocity
  w0 ,
• determine the angular velocity of the assembly
  after the
• panel has been released and comes to rest against
  the
• plate.
• I for a plate on edge is (1/4)mr2 for (1/2) plate
  is (1/8)mr2
• IGw1 impulse IGw2

4

• Problem 17.71 A semicircular panel of radius r is
• attached with hinges to a circular plate of
  radius r and
• initially held in the vertical position as shown.
  The plate
• and panel are made of the same material and have
  the
• same thickness. Knowing that the entire assembly
  is
• rotating freely with an initial angular velocity
  w0 ,
• determine the angular velocity of the assembly
  after the
• panel has been released and comes to rest against
  the
• plate.
• I for a plate on edge is (1/4)mr2 for (1/2) plate
  is (1/8)mr2
• IGw1 impulse IGw2
• ((1/2)mr2 (1/8)mr2)w0

5

• Problem 17.71 A semicircular panel of radius r is
• attached with hinges to a circular plate of
  radius r and
• initially held in the vertical position as shown.
  The plate
• and panel are made of the same material and have
  the
• same thickness. Knowing that the entire assembly
  is
• rotating freely with an initial angular velocity
  w0 ,
• determine the angular velocity of the assembly
  after the
• panel has been released and comes to rest against
  the
• plate.
• I for a plate on edge is (1/4)mr2 for (1/2) plate
  is (1/8)mr2
• IGw1 impulse IGw2
• ((1/2)mr2 (1/8)mr2)w0 0

6

• Problem 17.71 A semicircular panel of radius r is
• attached with hinges to a circular plate of
  radius r and
• initially held in the vertical position as shown.
  The plate
• and panel are made of the same material and have
  the
• same thickness. Knowing that the entire assembly
  is
• rotating freely with an initial angular velocity
  w0 ,
• determine the angular velocity of the assembly
  after the
• panel has been released and comes to rest against
  the
• plate.
• I for a plate on edge is (1/4)mr2 for (1/2) plate
  is (1/8)mr2
• IGw1 impulse IGw2
• ((1/2)mr2 (1/8)mr2)w0 0 ((1/2)mr2
  (1/4)mr2)w2

7

• Problem 17.71 A semicircular panel of radius r is
• attached with hinges to a circular plate of
  radius r and
• initially held in the vertical position as shown.
  The plate
• and panel are made of the same material and have
  the
• same thickness. Knowing that the entire assembly
  is
• rotating freely with an initial angular velocity
  w0 ,
• determine the angular velocity of the assembly
  after the
• panel has been released and comes to rest against
  the
• plate.
• I for a plate on edge is (1/4)mr2 for (1/2) plate
  is (1/8)mr2
• IGw1 impulse IGw2
• ((1/2)mr2 (1/8)mr2)w0 0 ((1/2)mr2
  (1/4)mr2)w2
• (5/8)w0 (3/4)w2
• w2 (5/6)w0

8

• Problem 17.85 A 3 kg uniform cylinder A can roll
• without sliding on a 5 kg cart C and is attached
  to
• a spring AB of constant k 100 N/m as shown.
• The system is released from rest when the spring
• is stretched .02 m. neglecting wheel friction,
• determine the velocity of the cart and the
  angular
• velocity of the cylinder when the spring first
• reaches its undeformed state.

9

• Problem 17.85 A 3 kg uniform cylinder A can roll
• without sliding on a 5 kg cart C and is attached
  to
• a spring AB of constant k 100 N/m as shown.
• The system is released from rest when the spring
• is stretched .02 m. neglecting wheel friction,
• determine the velocity of the cart and the
  angular
• velocity of the cylinder when the spring first
• reaches its undeformed state.
• L1X impulse in x L2X
• 0 0 3vA 5vC

10

• Problem 17.85 A 3 kg uniform cylinder A can roll
• without sliding on a 5 kg cart C and is attached
  to
• a spring AB of constant k 100 N/m as shown.
• The system is released from rest when the spring
• is stretched .02 m. neglecting wheel friction,
• determine the velocity of the cart and the
  angular
• velocity of the cylinder when the spring first
• reaches its undeformed state.
• L1X impulse in x L2X
• 0 0 3vA 5vC ? vA - (5/3)vC

11

• Problem 17.85 A 3 kg uniform cylinder A can roll
• without sliding on a 5 kg cart C and is attached
  to
• a spring AB of constant k 100 N/m as shown.
• The system is released from rest when the spring
• is stretched .02 m. neglecting wheel friction,
• determine the velocity of the cart and the
  angular
• velocity of the cylinder when the spring first
• reaches its undeformed state.
• L1X impulse in x L2X
• 0 0 3vA 5vC ? vA - (5/3)vC
• T1 0,

12

• Problem 17.85 A 3 kg uniform cylinder A can roll
• without sliding on a 5 kg cart C and is attached
  to
• a spring AB of constant k 100 N/m as shown.
• The system is released from rest when the spring
• is stretched .02 m. neglecting wheel friction,
• determine the velocity of the cart and the
  angular
• velocity of the cylinder when the spring first
• reaches its undeformed state.
• L1X impulse in x L2X
• 0 0 3vA 5vC ? vA - (5/3)vC
• T1 0, V1 (1/2)100(.02)2 .02 ,

13

• Problem 17.85 A 3 kg uniform cylinder A can roll
• without sliding on a 5 kg cart C and is attached
  to
• a spring AB of constant k 100 N/m as shown.
• The system is released from rest when the spring
• is stretched .02 m. neglecting wheel friction,
• determine the velocity of the cart and the
  angular
• velocity of the cylinder when the spring first
• reaches its undeformed state.
• L1X impulse in x L2X
• 0 0 3vA 5vC ? vA - (5/3)vC
• T1 0, V1 (1/2)100(.02)2 .02 , V2
  0,

14

• Problem 17.85 A 3 kg uniform cylinder A can roll
• without sliding on a 5 kg cart C and is attached
  to
• a spring AB of constant k 100 N/m as shown.
• The system is released from rest when the spring
• is stretched .02 m. neglecting wheel friction,
• determine the velocity of the cart and the
  angular
• velocity of the cylinder when the spring first
• reaches its undeformed state.
• L1X impulse in x L2X
• 0 0 3vA 5vC ? vA - (5/3)vC
• T1 0, V1 (1/2)100(.02)2 .02 , V2
  0,
• T2 (1/2)5vC2 (1/2)3vA2 (1/2)((1/2)3(.15)2)w2
  

15

• Problem 17.85 A 3 kg uniform cylinder A can roll
• without sliding on a 5 kg cart C and is attached
  to
• a spring AB of constant k 100 N/m as shown.
• The system is released from rest when the spring
• is stretched .02 m. neglecting wheel friction,
• determine the velocity of the cart and the
  angular
• velocity of the cylinder when the spring first
• reaches its undeformed state.
• L1X impulse in x L2X
• 0 0 3vA 5vC ? vA - (5/3)vC
• T1 0, V1 (1/2)100(.02)2 .02 , V2
  0,
• T2 (1/2)5vC2 (1/2)3vA2 (1/2)((1/2)3(.15)2)w2
  
• T2 (5/2)vC2 (3/2)vA2 (3/4)(.15)2w2

16

• Problem 17.85 A 3 kg uniform cylinder A can roll
• without sliding on a 5 kg cart C and is attached
  to
• a spring AB of constant k 100 N/m as shown.
• The system is released from rest when the spring
• is stretched .02 m. neglecting wheel friction,
• determine the velocity of the cart and the
  angular
• velocity of the cylinder when the spring first
• reaches its undeformed state.
• L1X impulse in x L2X
• 0 0 3vA 5vC ? vA - (5/3)vC
• T1 0, V1 (1/2)100(.02)2 .02 , V2
  0,
• T2 (1/2)5vC2 (1/2)3vA2 (1/2)((1/2)3(.15)2)w2
  
• T2 (5/2)vC2 (3/2)vA2 (3/4)(.15)2w2
• T1 V1 T2 V2
• 0 .02 (5/2)vC2 (3/2)vA2 (3/4)(.15)2w2 0

17

• Problem 17.85 A 3 kg uniform cylinder A can roll
• without sliding on a 5 kg cart C and is attached
  to
• a spring AB of constant k 100 N/m as shown.
• The system is released from rest when the spring
• is stretched .02 m. neglecting wheel friction,
• determine the velocity of the cart and the
  angular
• velocity of the cylinder when the spring first
• reaches its undeformed state.
• L1X impulse in x L2X
• 0 0 3vA 5vC ? vA - (5/3)vC
• T1 0, V1 (1/2)100(.02)2 .02 , V2
  0,
• T2 (1/2)5vC2 (1/2)3vA2 (1/2)((1/2)3(.15)2)w2
  
• T2 (5/2)vC2 (3/2)vA2 (3/4)(.15)2w2
• T1 V1 T2 V2
• 0 .02 (5/2)vC2 (3/2)vA2 (3/4)(.15)2w2 0
• vA vC wk x .15j

18

• Problem 17.85 A 3 kg uniform cylinder A can roll
• without sliding on a 5 kg cart C and is attached
  to
• a spring AB of constant k 100 N/m as shown.
• The system is released from rest when the spring
• is stretched .02 m. neglecting wheel friction,
• determine the velocity of the cart and the
  angular
• velocity of the cylinder when the spring first
• reaches its undeformed state.
• L1X impulse in x L2X
• 0 0 3vA 5vC ? vA - (5/3)vC
• T1 0, V1 (1/2)100(.02)2 .02 , V2
  0,
• T2 (1/2)5vC2 (1/2)3vA2 (1/2)((1/2)3(.15)2)w2
  
• T2 (5/2)vC2 (3/2)vA2 (3/4)(.15)2w2
• T1 V1 T2 V2
• 0 .02 (5/2)vC2 (3/2)vA2 (3/4)(.15)2w2 0
• vA vC wk x .15j ? vA vC - .15w

19

• Problem 17.85 A 3 kg uniform cylinder A can roll
• without sliding on a 5 kg cart C and is attached
  to
• a spring AB of constant k 100 N/m as shown.
• The system is released from rest when the spring
• is stretched .02 m. neglecting wheel friction,
• determine the velocity of the cart and the
  angular
• velocity of the cylinder when the spring first
• reaches its undeformed state.
• L1X impulse in x L2X
• 0 0 3vA 5vC ? vA - (5/3)vC
• T1 0, V1 (1/2)100(.02)2 .02 , V2
  0,
• T2 (1/2)5vC2 (1/2)3vA2 (1/2)((1/2)3(.15)2)w2
  
• T2 (5/2)vC2 (3/2)vA2 (3/4)(.15)2w2
• T1 V1 T2 V2
• 0 .02 (5/2)vC2 (3/2)vA2 (3/4)(.15)2w2 0
• vA vC wk x .15j ? vA vC - .15w
• - (5/3)vC vC - .15w

20

• Problem 17.85 A 3 kg uniform cylinder A can roll
• without sliding on a 5 kg cart C and is attached
  to
• a spring AB of constant k 100 N/m as shown.
• The system is released from rest when the spring
• is stretched .02 m. neglecting wheel friction,
• determine the velocity of the cart and the
  angular
• velocity of the cylinder when the spring first
• reaches its undeformed state.
• L1X impulse in x L2X
• 0 0 3vA 5vC ? vA - (5/3)vC
• T1 0, V1 (1/2)100(.02)2 .02 , V2
  0,
• T2 (1/2)5vC2 (1/2)3vA2 (1/2)((1/2)3(.15)2)w2
  
• T2 (5/2)vC2 (3/2)vA2 (3/4)(.15)2w2
• T1 V1 T2 V2
• 0 .02 (5/2)vC2 (3/2)vA2 (3/4)(.15)2w2 0
• vA vC wk x .15j ? vA vC - .15w
• - (5/3)vC vC - .15w ? w (160/9)vC

21

• Problem 17.85 A 3 kg uniform cylinder A can roll
• without sliding on a 5 kg cart C and is attached
  to
• a spring AB of constant k 100 N/m as shown.
• The system is released from rest when the spring
• is stretched .02 m. neglecting wheel friction,
• determine the velocity of the cart and the
  angular
• velocity of the cylinder when the spring first
• reaches its undeformed state.
• L1X impulse in x L2X
• 0 0 3vA 5vC ? vA - (5/3)vC
• T1 0, V1 (1/2)100(.02)2 .02 , V2
  0,
• T2 (1/2)5vC2 (1/2)3vA2 (1/2)((1/2)3(.15)2)w2
  
• T2 (5/2)vC2 (3/2)vA2 (3/4)(.15)2w2
• T1 V1 T2 V2
• 0 .02 (5/2)vC2 (3/2)vA2 (3/4)(.15)2w2 0
• vA vC wk x .15j ? vA vC - .15w
• - (5/3)vC vC - .15w ? w (160/9)vC
• .02(5/2)vC2(3/2)(- (5/3)vC)2(3/4)(.15)2((160/9)
  vC)2

22

• Problem 17.85 A 3 kg uniform cylinder A can roll
• without sliding on a 5 kg cart C and is attached
  to
• a spring AB of constant k 100 N/m as shown.
• The system is released from rest when the spring
• is stretched .02 m. neglecting wheel friction,
• determine the velocity of the cart and the
  angular
• velocity of the cylinder when the spring first
• reaches its undeformed state.
• L1X impulse in x L2X
• 0 0 3vA 5vC ? vA - (5/3)vC
• T1 0, V1 (1/2)100(.02)2 .02 , V2
  0,
• T2 (1/2)5vC2 (1/2)3vA2 (1/2)((1/2)3(.15)2)w2
  
• T2 (5/2)vC2 (3/2)vA2 (3/4)(.15)2w2
• T1 V1 T2 V2
• 0 .02 (5/2)vC2 (3/2)vA2 (3/4)(.15)2w2 0
• vA vC wk x .15j ? vA vC - .15w
• - (5/3)vC vC - .15w ? w (160/9)vC
• .02(5/2)vC2(3/2)(- (5/3)vC)2(3/4)(.15)2((160/9)
  vC)2
• vC - .04082 m/s w -.726 rad/s

23

• Problem 17-72 Two .36 kg balls are put
• successively into the center C of the slender 1.8
• kg tube AB. Knowing that when the first ball is
• put into the tube the initial angular velocity of
  the
• tube is 8 rad/s and neglecting the effect of
• friction, determine the angular velocity of the
• tube just after (a) the first ball has left the
  tube,
• (b) the second ball has left the tube.

24

• Problem 17-72 Two .36 kg balls are put
• successively into the center C of the slender 1.8
• kg tube AB. Knowing that when the first ball is
• put into the tube the initial angular velocity of
  the
• tube is 8 rad/s and neglecting the effect of
• friction, determine the angular velocity of the
• tube just after (a) the first ball has left the
  tube,
• (b) the second ball has left the tube.
• H1 Imp12 H2

25

• Problem 17-72 Two .36 kg balls are put
• successively into the center C of the slender 1.8
• kg tube AB. Knowing that when the first ball is
• put into the tube the initial angular velocity of
  the
• tube is 8 rad/s and neglecting the effect of
• friction, determine the angular velocity of the
• tube just after (a) the first ball has left the
  tube,
• (b) the second ball has left the tube.
• H1 Imp12 H2
• I1w1 Imp12 I2w2

26

• Problem 17-72 Two .36 kg balls are put
• successively into the center C of the slender 1.8
• kg tube AB. Knowing that when the first ball is
• put into the tube the initial angular velocity of
  the
• tube is 8 rad/s and neglecting the effect of
• friction, determine the angular velocity of the
• tube just after (a) the first ball has left the
  tube,
• (b) the second ball has left the tube.
• H1 Imp12 H2
• I1w1 Imp12 I2w2
• (1/12)1.8(.72)28

27

• Problem 17-72 Two .36 kg balls are put
• successively into the center C of the slender 1.8
• kg tube AB. Knowing that when the first ball is
• put into the tube the initial angular velocity of
  the
• tube is 8 rad/s and neglecting the effect of
• friction, determine the angular velocity of the
• tube just after (a) the first ball has left the
  tube,
• (b) the second ball has left the tube.
• H1 Imp12 H2
• I1w1 Imp12 I2w2
• (1/12)1.8(.72)28 0

28

• Problem 17-72 Two .36 kg balls are put
• successively into the center C of the slender 1.8
• kg tube AB. Knowing that when the first ball is
• put into the tube the initial angular velocity of
  the
• tube is 8 rad/s and neglecting the effect of
• friction, determine the angular velocity of the
• tube just after (a) the first ball has left the
  tube,
• (b) the second ball has left the tube.
• H1 Imp12 H2
• I1w1 Imp12 I2w2
• (1/12)1.8(.72)28 0((1/12)1.8(.72)2
  .36(.36)2)w2

29

• Problem 17-72 Two .36 kg balls are put
• successively into the center C of the slender 1.8
• kg tube AB. Knowing that when the first ball is
• put into the tube the initial angular velocity of
  the
• tube is 8 rad/s and neglecting the effect of
• friction, determine the angular velocity of the
• tube just after (a) the first ball has left the
  tube,
• (b) the second ball has left the tube.
• H1 Imp12 H2
• I1w1 Imp12 I2w2
• (1/12)1.8(.72)28 0((1/12)1.8(.72)2
  .36(.36)2)w2
• w2 5 rad/s

30

• Problem 17-72 Two .36 kg balls are put
• successively into the center C of the slender 1.8
• kg tube AB. Knowing that when the first ball is
• put into the tube the initial angular velocity of
  the
• tube is 8 rad/s and neglecting the effect of
• friction, determine the angular velocity of the
• tube just after (a) the first ball has left the
  tube,
• (b) the second ball has left the tube.
• H1 Imp12 H2
• I1w1 Imp12 I2w2
• (1/12)1.8(.72)28 0((1/12)1.8(.72)2
  .36(.36)2)w2
• w2 5 rad/s
• (1/12)1.8(.72)250 ((1/12)1.8(.72)2 .36(.36)2)w3

31

• Problem 17-72 Two .36 kg balls are put
• successively into the center C of the slender 1.8
• kg tube AB. Knowing that when the first ball is
• put into the tube the initial angular velocity of
  the
• tube is 8 rad/s and neglecting the effect of
• friction, determine the angular velocity of the
• tube just after (a) the first ball has left the
  tube,
• (b) the second ball has left the tube.
• H1 Imp12 H2
• I1w1 Imp12 I2w2
• ((1/12)1.8(.72)28 0((1/12)1.8(.72)2
  .36(.36)2)w2
• w2 5 rad/s
• (1/12)1.8(.72)250 ((1/12)1.8(.72)2
  .36(.36)2)w3
• w3 3.13 rad/s

32

• Problem 17-72 Two .36 kg balls are put
• successively into the center C of the slender 1.8
• kg tube AB. Knowing that when the first ball is
• put into the tube the initial angular velocity of
  the
• tube is 8 rad/s and neglecting the effect of
• friction, determine the angular velocity of the
• tube just after (a) the first ball has left the
  tube,
• (b) the second ball has left the tube.
• H1 Imp12 H2
• I1w1 Imp12 I2w2
• (1/12)1.8(.72)28 0((1/12)1.8(.72)2
  .36(.36)2)w2
• w2 5 rad/s
• (1/12)1.8(.72)250 ((1/12)1.8(.72)2
  .36(.36)2)w3
• w3 3.13 rad/s
• What is the velocity of the ball relative to the
  tube
• When it exits ?

33

• Problem 17-72 Two .36 kg balls are put
• successively into the center C of the slender 1.8
• kg tube AB. Knowing that when the first ball is
• put into the tube the initial angular velocity of
  the
• tube is 8 rad/s and neglecting the effect of
• friction, determine the angular velocity of the
• tube just after (a) the first ball has left the
  tube,
• (b) the second ball has left the tube.
• H1 Imp12 H2
• I1w1 Imp12 I2w2
• (1/12)1.8(.72)28 0((1/12)1.8(.72)2
  .36(.36)2)w2
• w2 5 rad/s
• (1/12)1.8(.72)250 ((1/12)1.8(.72)2
  .36(.36)2)w3
• w3 3.13 rad/s
• What is the velocity of the ball relative to the
  tube
• When it exits ?

34

• Problem 17-72 Two .36 kg balls are put
• successively into the center C of the slender 1.8
• kg tube AB. Knowing that when the first ball is
• put into the tube the initial angular velocity of
  the
• tube is 8 rad/s and neglecting the effect of
• friction, determine the angular velocity of the
• tube just after (a) the first ball has left the
  tube,
• (b) the second ball has left the tube.
• H1 Imp12 H2
• I1w1 Imp12 I2w2
• (1/12)1.8(.72)28 0((1/12)1.8(.72)2
  .36(.36)2)w2
• w2 5 rad/s
• (1/12)1.8(.72)250 ((1/12)1.8(.72)2
  .36(.36)2)w3
• w3 3.13 rad/s
• What is the velocity of the ball relative to the
  tube
• When it exits ?
• T1 V1 T2 V2

35

• Problem 17-72 Two .36 kg balls are put
• successively into the center C of the slender 1.8
• kg tube AB. Knowing that when the first ball is
• put into the tube the initial angular velocity of
  the
• tube is 8 rad/s and neglecting the effect of
• friction, determine the angular velocity of the
• tube just after (a) the first ball has left the
  tube,
• (b) the second ball has left the tube.
• H1 Imp12 H2
• I1w1 Imp12 I2w2
• (1/12)1.8(.72)28 0((1/12)1.8(.72)2
  .36(.36)2)w2
• w2 5 rad/s
• (1/12)1.8(.72)250 ((1/12)1.8(.72)2
  .36(.36)2)w3
• w3 3.13 rad/s
• What is the velocity of the ball relative to the
  tube
• When it exits ?
• T1 V1 T2 V2
• (1/2)((1/12)1.8(.72)2)82 0

36

• Problem 17-72 Two .36 kg balls are put
• successively into the center C of the slender 1.8
• kg tube AB. Knowing that when the first ball is
• put into the tube the initial angular velocity of
  the
• tube is 8 rad/s and neglecting the effect of
• friction, determine the angular velocity of the
• tube just after (a) the first ball has left the
  tube,
• (b) the second ball has left the tube.
• H1 Imp12 H2
• I1w1 Imp12 I2w2
• (1/12)1.8(.72)28 0((1/12)1.8(.72)2
  .36(.36)2)w2
• w2 5 rad/s
• (1/12)1.8(.72)250 ((1/12)1.8(.72)2
  .36(.36)2)w3
• w3 3.13 rad/s
• What is the velocity of the ball relative to the
  tube
• When it exits ?
• T1 V1 T2 V2
• (1/2)((1/12)1.8(.72)2)82 0
• (1/2)((1/12)1.8(.72)2.36(.36)2)52
  (1/2).36v2

37

• Problem 17-72 Two .36 kg balls are put
• successively into the center C of the slender 1.8
• kg tube AB. Knowing that when the first ball is
• put into the tube the initial angular velocity of
  the
• tube is 8 rad/s and neglecting the effect of
• friction, determine the angular velocity of the
• tube just after (a) the first ball has left the
  tube,
• (b) the second ball has left the tube.
• H1 Imp12 H2
• I1w1 Imp12 I2w2
• (1/12)1.8(.72)28 0((1/12)1.8(.72)2
  .36(.36)2)w2
• w2 5 rad/s
• (1/12)1.8(.72)250 ((1/12)1.8(.72)2
  .36(.36)2)w3
• w3 3.13 rad/s
• What is the velocity of the ball relative to the
  tube
• When it exits ?
• T1 V1 T2 V2
• (1/2)((1/12)1.8(.72)2)82 0
• (1/2)((1/12)1.8(.72)2.36(.36)2)52
  (1/2).36v2

38

• Problem 17-72 Two .36 kg balls are put
• successively into the center C of the slender 1.8
• kg tube AB. Knowing that when the first ball is
• put into the tube the initial angular velocity of
  the
• tube is 8 rad/s and neglecting the effect of
• friction, determine the angular velocity of the
• tube just after (a) the first ball has left the
  tube,
• (b) the second ball has left the tube.
• H1 Imp12 H2
• I1w1 Imp12 I2w2
• (1/12)1.8(.72)28 0((1/12)1.8(.72)2
  .36(.36)2)w2
• w2 5 rad/s
• (1/12)1.8(.72)250 ((1/12)1.8(.72)2
  .36(.36)2)w3
• w3 3.13 rad/s
• What is the velocity of the ball relative to the
  tube
• When it exits ?
• T1 V1 T2 V2
• (1/2)((1/12)1.8(.72)2)52 0
• (1/2)((1/12)1.8(.72)2.36(.36)2)52
  (1/2).36v2

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