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physics

mechanics

Easy

Question

$text A man stands on a rotating platform with his arms stretched holding a end text 5 kg text weight in each end text text hand. The angular speed of the platform is 1.2revs end text to the power of negative 1 end exponent text . The moment of inertia of the man together end text text with the platform may be taken to be constant and equal to end text 6 kgm squared text . If the man brings his arms end text c l o s e space t o space h i s space c h e s t space w i t h space t h e space d i s tan c e space n space e a c h space w e i g h t space f r o m space t h e space a x i s space c h a n g i n g space f r o m space 100 space c m space t o space 20 c m. space T h e space n e w space a n g u l a r space s p e e d space o f space t h e space p l a t f o r m space i s$

$2 rev s^{- 1}$
$3 rev s^{- 1}$
$5 rev s^{- 1}$
$6 rev s^{- 1}$

The correct answer is: $3 rev s^{- 1}$

$I subscript 1 equals 6 plus 2 cross times 5 cross times left parenthesis 1 right parenthesis squared equals 16 kgm squared straight omega subscript 1 equals 1.2 revs to the power of negative 1 end exponent straight L subscript 1 equals straight I subscript 1 straight omega subscript 1 straight I subscript 2 equals 6 plus 2 cross times 5 cross times left parenthesis 0.2 right parenthesis squared equals 6.4 kgm squared straight L subscript 1 equals straight L subscript 2 text or end text straight I subscript 1 straight omega subscript 1 equals straight I subscript 2 straight omega subscript 2 bold omega subscript bold 2 bold equals fraction numerator bold I subscript bold 1 bold omega subscript bold 1 over denominator bold I subscript bold 2 end fraction bold equals fraction numerator begin bold style left parenthesis 16 kgm squared right parenthesis end style begin bold style left parenthesis 1.2 revs to the power of negative 1 end exponent right parenthesis end style over denominator begin bold style left parenthesis 6.4 kgm squared right parenthesis end style end fraction bold equals bold 3 bold revs to the power of bold minus bold 1 end exponent$

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$text Two discs of moments of inertia end text I subscript 1 text and end text I subscript 2 text about their respective axes, rotating with angular end text text frequencies, end text omega subscript 1 text and end text omega subscript 2 text respectively, are brought into contact face to face with their axes of end text text rotation coincident. The angular frequency of the composite disc will be A end text$

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$text A circular platform is mounted on a vertical frictionless axle. Its radius is end text r equals 2 m text and its moment end text text of inertia end text straight I equals 200 kgm squared text . It is initially at rest. A end text 70 kg text man stands on the edge of the platform and end text text begins to walk along the edge at speed end text v subscript 0 equals 1 ms to the power of negative 1 end exponent text relative to the ground. The angular velocity end text text of the platform is end text$

$text A circular platform is mounted on a vertical frictionless axle. Its radius is end text r equals 2 m text and its moment end text text of inertia end text straight I equals 200 kgm squared text . It is initially at rest. A end text 70 kg text man stands on the edge of the platform and end text text begins to walk along the edge at speed end text v subscript 0 equals 1 ms to the power of negative 1 end exponent text relative to the ground. The angular velocity end text text of the platform is end text$

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PhysicsMechanics

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A particle of mass M may move with the velocity v, along AO, or DE or statements is not correct about particle’s angular momentum about point O.

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PhysicsMechanics

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PhysicsMechanics

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PhysicsMechanics

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