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Physics

Mechanics

Easy

Question

$text A uniform circular disc of mass end text straight M text and radius end text straight R text rolls without slipping on a horizontal surface end text text If the velocity of its centre is end text v subscript 0 comma text then the total angular momentum of the disc about a fixed end text text point end text P text at a height end text 3 straight R divided by 2 text about the centre end text straight C text . end text$

Increase continuously as the disc moves away
Decrease continuously as the disc moves away
$Is always equal to 2 M R v_{0}$
$Is always equal to M R v$

The correct answer is: $text Is always equal to end text M R v$

$L equals I subscript c m end subscript omega with not stretchy rightwards arrow on top plus m v with not stretchy rightwards arrow on top subscript c m end subscript r with not stretchy rightwards arrow on top equals fraction numerator M R squared over denominator 2 end fraction times omega left parenthesis negative k with not stretchy hat on top right parenthesis plus M times 3 over 2 R left parenthesis negative j with not stretchy hat on top right parenthesis cross times v subscript 0 i with not stretchy hat on top L equals M R v subscript 0 left parenthesis k with not stretchy hat on top right parenthesis$

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$text Consider a body, shown in the figure, consisting of two identical balls, each of mass M end text text connected by a light rigid rod. If an impulse end text J equals M V text is imparted to the body at one of its ends, what would be end text i t s space a n g u l a r space m o t i o n$

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$text A composite rod comprising two rods of mass end text straight m text and end text 2 straight m text and each of length end text l equals 1 straight m text as shown in the end text text figure. Assume end text omega equals 10 rad divided by straight s text and end text straight m equals 1 kg comma text the end text KE text of the rotating composite rod is end text$

$text A composite rod comprising two rods of mass end text straight m text and end text 2 straight m text and each of length end text l equals 1 straight m text as shown in the end text text figure. Assume end text omega equals 10 rad divided by straight s text and end text straight m equals 1 kg comma text the end text KE text of the rotating composite rod is end text$

PhysicsMechanics

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

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

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

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

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$A space c h i l d space i s space s tan d i n g space w i t h space h i s space t w o space a r m s space o u t s t r e t c h e d space a t space t h e space c e n t r e space o f space a space t u r n t a b l e space t h a t space i s space r o t a t i n g space a b o u t space i t s space c e n t r a l space a x i s space w i t h space a n space a n g u l a r space s p e e d space omega subscript 0 space. space N o w comma space t h e space c h i l d space f o l d s space h i s space h a n d s space b a c k space s o space t h a t space m o m e n t space o f space i n e r t i a space b e c o m e s space 3 space t i m e s space t h e space i n i t i a l space v a l u e. space T h e space n e w space a n g u l a r space s p e e d space i s$

$A space c h i l d space i s space s tan d i n g space w i t h space h i s space t w o space a r m s space o u t s t r e t c h e d space a t space t h e space c e n t r e space o f space a space t u r n t a b l e space t h a t space i s space r o t a t i n g space a b o u t space i t s space c e n t r a l space a x i s space w i t h space a n space a n g u l a r space s p e e d space omega subscript 0 space. space N o w comma space t h e space c h i l d space f o l d s space h i s space h a n d s space b a c k space s o space t h a t space m o m e n t space o f space i n e r t i a space b e c o m e s space 3 space t i m e s space t h e space i n i t i a l space v a l u e. space T h e space n e w space a n g u l a r space s p e e d space i s$

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$text A solid cylinder of mass end text 20 kg text and radius end text 20 cm text rotates about its axis with a angular speed end text 100 text rad end text s to the power of negative 1 end exponent. text The angular momentum of the cylinder about its axis is end text$

$text A solid cylinder of mass end text 20 kg text and radius end text 20 cm text rotates about its axis with a angular speed end text 100 text rad end text s to the power of negative 1 end exponent. text The angular momentum of the cylinder about its axis is end text$

PhysicsMechanics

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

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

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