physics

mechanics

Easy

Question

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

$r α$
$\sqrt{(a + r α)^{2} + {(r ω^{2})}^{2}}$
$\sqrt{r^{2} α^{2} + r^{2} ω^{4}}$
$\frac{a r}{R}$

The correct answer is: $\sqrt{(a + r α)^{2} + {(r ω^{2})}^{2}}$

$a with rightwards arrow on top subscript o with bar on top end subscript equals a i with hat on top comma a with rightwards arrow on top subscript p divided by a end subscript equals alpha r i with hat on top plus omega squared r left parenthesis negative j with hat on top right parenthesis a with rightwards arrow on top subscript p with bar on top end subscript equals a with rightwards arrow on top subscript sigma with bar on top end subscript plus a with rightwards arrow on top subscript negative p divided by o end subscript equals left parenthesis stack a plus alpha r with bar on top right parenthesis i with hat on top plus omega squared r j with hat on top a with rightwards arrow on top subscript p with bar on top end subscript equals square root of left parenthesis stack a plus alpha r with bar on top right parenthesis squared plus open parentheses stack omega squared r with bar on top close parentheses squared end root$

$I n space f i g u r e comma space w h e e l space A space o f space r a d i u s space r subscript A equals 10 space c m space i s space c o u p l e d space b y space b e l t space B space t o space w h e e l space C space o f space r a d i u s space r subscript C equals space 25 space c m. space T h e space a n g u l a r space s p e e d space o f space w h e e l space A space i s space i n c r e a s e d space f r o m space r e s t space a t a space c o n s tan t space r a t e space o f space 1.6 space r a d space divided by space s squared. space F i n d space t h e space t i m e space n e e d e d space f o r space w h e e l space C space t o space r e a c h space a n space a n g u l a r space s p e e d space o f space 12.8 space r a d space divided by space s comma space a s s u m i n g space t h e space b e l t space d o e s space n o t space s l i p.$

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Mechanics

Physics

$A space d i v e r space m a k e s space 2.5 space r e v o l u t i o n s space o n space t h e space w a y space f r o m space a space 10 minus space m space minus h i g h space p l a t f o r m space t o space t h e space w a t e r. space A s s u m i n g space z e r o space i n i t i a l space v e r t i c a l space v e l o c i t y comma space t h e space a v e r a g e space a n g u l a r space v e l o c i t y space d u r i n g space t h e space d i v e space i s$

PhysicsMechanics

Mechanics

Physics

$I n space p r e v i o u s space p r o b l e m comma space t h e space c a r apostrophe s space f u e l space e c o n o m y space i n space m i l e s space p e r space g a l l o n space o r space k m space divided by space L a p p e a r space t o space b e space h e t t e r$

PhysicsMechanics

Mechanics

Physics

$S u p p o s e space a space c a r apostrophe s space s tan d a r d space t i r e s space a r e space r e p l a c e d space w i t h space t i r e s space 1.50 space t i m e s space l a r g e r space i n space d i a m e t e r. space W i l l space t h e space c a r apostrophe s space s p e e d o m e t e r space r e a d i n g space b e$

PhysicsMechanics

Mechanics

Physics

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

PhysicsMechanics

Mechanics

Physics

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

PhysicsMechanics

Mechanics

Physics

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

PhysicsMechanics

Mechanics

Physics

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

PhysicsMechanics

Mechanics

Physics

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

PhysicsMechanics

Mechanics

Physics

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

PhysicsMechanics

Mechanics

Physics

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

PhysicsMechanics

Mechanics

Physics

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

PhysicsMechanics

Mechanics

Physics

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

PhysicsMechanics

Mechanics

Physics

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

PhysicsMechanics

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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