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Lecture  30:  Rigid-­‐body  Rotation  about  a  Moving  Axis

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Lecture  Objectives  1.  Compare  translational  and  rotational  kinetic  energies  of  a  rolling  object.  2.  Apply  Newton’s  second  law  of  rotation  and  conservation  of  energy  to  physical  systems  that  involves  rotation  about  a  moving  axis.    

Rigid-­‐body  rotation  about  a  moving  axis

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Speed  of  a  primitive  yo-­‐yo

Given:  mass,  M  radius,  R  height,  h  target  variable,  vcm 7

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Solution:  U1  =  mgh,  U2  =  0  K1  =  0  I  =  1/2  MR2

Race  of  the  rolling  objects

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Solution:  U1  =  mgh,  U2  =  0  K1  =  0  I  =  cMR2

Acceleration  of  a  rolling  sphere

Given:  Isolid  sphere  =  2/5  MR2  

Angle  of  inclination,    target  variables,  acm-­‐x  and  f

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FBD  of  the  solid  ball

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Equations  of  Motion

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Rolling  without  slipping  so  may  write  (2)  as

(1)

(2)

Solve  for  f  in  (1)  and  substitute  to  (2):

(3)

(4)

(5)

Work  in  rotational  motion

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Work  in  rotational  motion

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Power  in  rotational  motion

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Seatwork

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Seatwork  1

Note:    1rev  =  2πrad

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Seatwork  

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Seatwork  (yes  or  no)

4.Is   it   possible   to   change   the   translational   kinetic  energy   of   an   object   without   changing   its   rotational  energy?    

5.Must   an   object   be   rotating   to   have   a   non-­‐zero  moment  of  inertia?

Seatwork  answers

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Seatwork  1

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Seatwork  

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Seatwork  (yes  or  no)

4.Is   it   possible   to   change   the   translational   kinetic  energy   of   an   object   without   changing   its   rotational  energy?  NO;  v  =  Rω  

5.Must   an   object   be   rotating   to   have   a   non-­‐zero  moment  of  inertia?  NO;  ex:  I  =  mR2  (no  rotation)