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Prof Walter Lewin, Massachusetts Institute of Technology (MIT) (MA), Physics, Classical Mechanics, Final Exam Solution, cylindrical axis, gravitational acceleration, Friction, maximum displacement angle, period of oscillation.
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Massachusetts Institute of Technology Physics Department Physics Final Fall SOLUTIONS Problem p oints v 0 sin pts a vy v sin g t t (^0) g pts b y v v sin t (^0 0) g^ t
v 0 sin (^) v 0 sin y v 0 sin (^) g (^) g g 2 y v^ sin (^2) 0 g pts c v 0 v 0 sin pts d x v 0 v 0 cos t t (^) g v 20 sin cos x g
Problem p oints a mg l mv A^ vA l
pts g 2 pts b Net force up must b e macen m mg T mg mg T mg pts c gravity mg l tension vA l
Problem p oints
R pts b Ip Ic M b M M b
pts c p Ip bM g sin ^ M R^ M b^ bg (^1) R (^2) b 2 sin 2 pts d Under the small angle approximation sin and the equation bg of motion is given by ^ (^1) R 2 b^2 which is simple harmonic with
bg an angular frequency given by (^1) R 2 b 2 The p erio d is given by
(^1) R (^2) b 2 2 bg pts e There must b e a force at P or the CM would accelerate straight downwards
Problem p oints pts a The diagram
pts b R v R v z 2 pts c a v R a 2 R x 2 pts d F^ ma F^ m 2 R 2 x pts e T sin m 2 R 2 T cos mg tan 2 R g 2
Problem p oints
mv ^ mM^ G^ v M G pts a R R v 0 pts b mv R sin � mV R (^) V (^0) sin � ^
0 R 2 mM G m 0 mM^ G pts d same as in c or
v
R R 2 pts e ^ mv ^ mM^ G^ ^ m v^0 mM^ G 0 R 2 R (^) M G 0 M G
v
Problem p oints pts a M V 0 pts b W W M g Fbuoy Fbuoy M g W 0 W M g M g W 0 W
W 0
Problem p oints
2
fr
F ma I no slipping Ffr ma R Ffr mR a a R Ffr mR ma ma a a
^ a a
^ a
