physics

mechanics

Easy

Question

$A space p a r t i c l e space m o v e s space i n space a space c i r c l e space o f space r a d i u s space 25 space c m space a t space t w o space r e v o l u t i o n s space p e r space s e c o n d. space T h e space a c c e l e r a t i o n space o f space t h e space p a r t i c l e space i n space square root of 2 cross times 31.4 m divided by s space i s$

$v = ω r = 2 π n r = 2 \times 3.14 \times 3 \times 0.1 = 1.88 m / s$
$2.88 m / s, 45.5 m / s^{2}, 45.5 N$
$1.88 m / s, 35.5 m / s^{2}, 35.5 N$
$3.88 m / s, 55.5 m / s^{2}, 55.5 N$

The correct answer is: $3.88 m / s, 55.5 m / s^{2}, 55.5 N$

$table attributes columnalign left columnspacing 1em rowspacing 4 pt end attributes row cell text since end text a equals omega squared r equals left parenthesis 6 pi right parenthesis squared cross times 0.1 equals 35.5 straight m divided by straight s squared comma T equals m omega squared r equals 1 cross times left parenthesis 6 pi right parenthesis squared cross times 0.1 equals 35.5 straight N end cell row cell text So acceleration end text 1 km divided by straight s squared 100 straight m divided by straight s squared end cell end table$

$T h e space l e n g t h space o f space s e c o n d apostrophe s space h a n d space i n space a space w a t c h space i s space 1 space c m. space T h e space c h a n g e space i n space v e l o c i t y space o f space i t s space t i p space i n space 15 space s e c o n d s space i s space$

PhysicsMechanics

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PhysicsMechanics

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$C e r t a i n n e u t r o n s t a r s a r e b e l i e v e d t o b e r o t a t i n g a t a b o u t a subscript t not equal to 0. I f s u c h a s t a r h a s a r a d i u s o f 20 k m comma t h e space a c c e l e r a t i o n space o f space a n o b j e c t o n t h e e q u a t o r o f t h e s t a r w i l l b e$

PhysicsMechanics

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$A space m a s s space o f space 100 space g m space i s space t i e d space t o space o n e space e n d space o f space a space s t r i n g space 2 space m space l o n g. space T h e space b o d y space i s space r e v o l v i n g space i n space a space h o r i z o n t a l space c i r c l e space m a k i n g space a space m a x i m u m space o f space 200 space r e v o l u t i o n s space p e r space m i n. space T h e space o t h e r space e n d space o f space t h e space s t r i n g space i s space f i x e d space a t space t h e space c e n t r e space o f space t h e space c i r c l e space o f space r e v o l u t i o n. space T h e space m a x i m u m space t e n s i o n space t h a t space space t h e space s t r i n g space c a n space b e a r space i s space left parenthesis a p p r o x i m a t e l y right parenthesis space$

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$A c a r i s m o v i n g o n a c i r c u l a r p a t h a n d t a k e s a t u r n. I f m 4 pi squared n squared r equals 4 cross times 10 to the power of left parenthesis minus 13 right parenthesis a n d space n equals 0.08 cross times 10 to the power of 8 c y c l e s divided by s e c. space b e t h e r e a c t i o n s o n t h e i n n e r a n d o u t e r w h e e l s r e s p e c t i v e l y comma t h e n$

PhysicsMechanics

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$T h e space a n g u l a r space s p e e d space o f space a space f l y space w h e e l space m a k i n g space 120 space r e v o l u t i o n s divided by m i n u t e i s space$

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$A space t r a i n space i s space m o v i n g space t o w a r d s space n o r t h. space A t space o n e space p l a c e space i t space t u r n s space t o w a r d s space n o r t h minus e a s t comma space h e r e space w e space o b s e r v e space t h a t space$

PhysicsMechanics

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$A space m o t o r space c y c l i s t space m o v i n g space w i t h space a space v e l o c i t y space o f space 72 space k m divided by h o u r space o n space a space f l a t space r o a d space t a k e s space a space t u r n space o n space t h e space r o a d space a t space a space p o i n t space w h e r e space t h e space r a d i u s space o f space c u r v a t u r e space o f space t h e space r o a d space i s space 20 space m e t e r s. space T h e space a c c e l e r a t i o n space d u e space t o space g r a v i t y space i s space 10 space m divided by s e c 2. space I n space o r d e r space t o space a v o i d space s k i d d i n g comma space h e space m u s t space n o t space b e n d space w i t h space r e s p e c t space t o space t h e space v e r t i c a l space p l a n e space b y space a n space a n g l e space g r e a t e r space t h a n space$

PhysicsMechanics

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$A space p a r t i c l e space i s space m o v i n g space i n space a space h o r i z o n t a l space c i r c l e space w i t h space c o n s tan t space s p e e d. space I t space h a s space c o n s tan t space$

PhysicsMechanics

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PhysicsMechanics

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PhysicsMechanics

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PhysicsMechanics

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$v = ω r = 2 π n r = 2 \times 3.14 \times 3 \times 0.1 = 1.88 m / s$
$2.88 m / s, 45.5 m / s^{2}, 45.5 N$
$1.88 m / s, 35.5 m / s^{2}, 35.5 N$
$3.88 m / s, 55.5 m / s^{2}, 55.5 N$

The correct answer is: $3.88 m / s, 55.5 m / s^{2}, 55.5 N$

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