physics

mechanics

Easy

Question

$A space g r i n d s t o n e space i n c r e a s e s space i n space a n g u l a r space s p e e d space f r o m space 4.00 space r a d space divided by space s space t o space 12.00 space r a d space divided by space s space i n 4.00 space s. space T h r o u g h space w h a t space a n g l e space d o e s space i t space t u r n space d u r i n g space t h a t space t i m e space i n t e r v a l space i f space t h e space a n g u l a r a c c e l e r a t i o n space i s space c o n s tan t ?$

$32.0 r a d$
$16.0 r a d$
$8.00 r a d$
$12.0 r a d$

The correct answer is: $32.0 r a d$

$T h e space a n g u l a r space d i s p l a c e m e n t space w i l l space b e table attributes columnalign left end attributes row cell capital delta theta equals omega subscript text avg end text end subscript capital delta t equals open parentheses fraction numerator omega subscript f plus omega subscript i over denominator 2 end fraction close parentheses capital delta t end cell row cell equals open parentheses fraction numerator 12.00 r a d divided by s plus 4.00 r a d divided by s over denominator 2 end fraction close parentheses left parenthesis 4.00 s right parenthesis equals 32.0 r a d end cell end table$

$P a r t i c l e space P space s h o w n space i n space f i g u r e space i s space m o v i n g space i n space a space c i r c l e space o f space r a d i u s space R equals 10 space c m space w i t h space l i n e a r space s p e e d space v equals 2 space m s to the power of negative 1 end exponent. space T h e space a n g u l a r space s p e e d space o f space p a r t i c l e space a b o u t space a space f i x e d space p o i n t space O space o n space t h e c i r c l e space i s$

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Mechanics

Physics

$A space c y c l i s t space r i d e s space a space b i c y c l e space w i t h space a space w h e e l space r a d i u s space o f space 0.500 space m space a c r o s s space c a m p u s. space A space p i e c e space o f space p l a s t i c space o n space t h e space f r o n t space r i m space m a k e s space a space c l i c k i n g space s o u n d space e v e r y space t i m e space i t space p a s s e s space t h r o u g h space t h e space f o r k. I f space t h e space c y c l i s t space c o u n t s space 320 space c l i c k s space b e t w e e n space h e r space a p a r t m e n t space a n d space t h e space c a f e t e r i a comma space h o w space f a r space h a s space s h e space t r a v e l l e d ?$

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Mechanics

Physics

$A space r i n g space o f space r a d i u s space R space r o l l s space w i t h o u t space s l i p p i n g space o n space a space r o u g h space h o r i z o n t a l space s u r f a c e space w i t h space a space c o n s tan t space v e l o c i t y. space T h e space r a d i u s space o f space c u r v a t u r e space o f space t h e space p a t h space f o l l o w e d space b y space a n y space p a r t i c l e o f space t h e space r i n g space a t space t h e space h i g h e s t space p o i n t space o f space i t s space p a t h space w i l l space b e colon$

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Mechanics

Physics

$W h e n space a space p e r s o n space t h r o w s space a space m e t e r space s t i c k space i t space i s space f o u n d space t h a t space t h e space c e n t r e space o f space t h e space s t i c k space i s m o v i n g space w i t h space s p e e d space 10 space m divided by s space a n d space l e f t space e n d space o f space s t i c k space w i t h space s p e e d space 20 space m divided by s. space B o t h space p o i n t s space m o v e space v e r t i c a l l y space u p w a r d s space a t space t h a t space m o m e n t. space T h e n space a n g u l a r space s p e e d space o f space t h e s t i c k space i s colon$

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Mechanics

Physics

$T w o space p o i n t s space o f space a space r o d space m o v e space w i t h space v e l o c i t i e s space 3 space v space a n d space p e r p e n d i c u l a r space t o space t h e space r o d space a n d space i n space t h e space s a m e space d i r e c t i o n comma space s e p a r a t e d space b y space a space d i s tan c e space apostrophe r apostrophe. space T h e n space t h e space a n g u l a r space v e l o c i t y space o f space t h e space r o d space i s colon$

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Mechanics

Physics

$I n space t h e space p u l l e y space s y s t e m space s h o w n comma space i f space r a d i i space o f space t h e space b i g g e r space a n d space s m a l l e r space p u l l e y space a r e space 2 space m space a n d 1 space m space r e s p e c t i v e l y space a n d space t h e space a c c e l e r a t i o n space o f space b l o c k space A space i s space 5 space m divided by s squared space i n space t h e space d o w n w a r d space d i r e c t i o n comma space t h e n space t h e space a c c e l e r a t i o n space o f space b l o c k space B space w i l l space b e colon$

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Mechanics

Physics

$T h e space a n g u l a r space v e l o c i t y space o f space a space r i g i d space b o d y space a b o u t space a n y space p o i n t space o f space t h a t space b o d y space i s space s a m e colon$

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Mechanics

Physics

$A n space a t h l e t e space t h r o w s space a space d i s c u s space f r o m space r e s t space t o space a space f i n a l space a n g u l a r space v e l o c i t y space o f space 15 space r a d space s to the power of negative 1 end exponent space i n 0.270 space s space b e f o r e space r e l e a sin g space i t. space D u r i n g space a c c e l e r a t i o n comma space d i s c u s space m o v e s space a space c i r c u l a r space a r c space o f space r a d i u s space 0.810 space m. space A c c e l e r a t i o n space o f space d i s c u s space b e f o r e space i t space i s space r e l e a s e d space i s$

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Mechanics

Physics

$A space f l y w h e e l space r o t a t i n g space a t space 420 space r p m space s l o w s space d o w n space a t space a space c o n s tan t space r a t e space o f space 2 space r a d space s to the power of negative 2 end exponent. space T h e space t i m e space r e q u i r e d space t o space s t o p space t h e space f l y w h e e l space i s$

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Mechanics

Physics

$text A railway truck of mass end text 10 to the power of 4 Kg text travelling at end text 1 ms to the power of negative 1 end exponent text collides with another of double its end text text mass moving in the opposite direction with velocity of end text 0.2 ms to the power of negative 1 end exponent text . If the trucks couple end text text automatically on collision, their common velocity in end text ms to the power of negative 1 end exponent text . end text$

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Mechanics

Physics

$text A moving body with a mass m end text subscript 1 text strikes a body of mass end text m subscript 2 text which is stationary. end text text Assuming perfectly elastic impact, the ratio end text m subscript 1 divided by m subscript 2 text so as to decrease the velocity of end text text first body end text 1.5 text times is end text$

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Mechanics

Physics

$text A mass end text m text moving horizontally (along the end text x text - axis) with velocity end text v text collides and sticks end text text to a mass of end text 3 m text moving vertically upward (along the end text y minus text axis) with velocity end text 2 v. text The end text text final velocity of the combination is end text$

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Mechanics

Physics

$text A bullet of mass end text m text is fired with a velocity end text v subscript 1 text at a body of mass end text M text moving in opposite end text text direction with velocity end text v subscript 2 text . The bullet penetrates the body and emerges with a velocity end text v. text The subsequent velocity of the body is end text$

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Mechanics

Physics

$text Two balls have masses in ratio 2:1. Their velocities are in the ratio of end text 1 colon 2 text . end text T h e space text coefficient of restitution is end text 5 over 6 text . Then the final velocity of each ball is end text$

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Mechanics

Physics

$T w o space p a r t i c l e s space o f space m a s s e s space m subscript 1 space a n d space m subscript 2 space a r e space c o n n e c t e d space b y space a space l i g h t space a n d space i n e x t e n s i b l e space s t r i n g space w h i c h space p a s s e s space o v e r space a space f i x e d space p u l l e y. space I n i t i a l l y comma space t h e space p a r t i c l e space m subscript 1 space m o v e s space w i t h space a space v e l o c i t y space v subscript 0 w h e n space t h e space s t r i n g space i s space n o t space t a u t. space N e g l e c t i n g space f r i c t i o n space i n space a l l space c o n t a c t i n g space s u r f a c e s comma space f i n d space t h e space v e l o c i t i e s space o f space t h e space p a r t i c l e s space m subscript 1 space a n d space m subscript 2 space j u s t space a f t e r space t h e space s t r i n g space i s space t a u t.$

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