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Mechanics

Physics

$I f space m space left parenthesis g plus pi n r squared right parenthesis space a n d space m left parenthesis g plus pi n r right parenthesis space r e p r e s e n t space r a d i a l space a n d space tan g e n t i a l space a c c e l e r a t i o n s comma space t h e space m o t i o n space o f space a space p a r t i c l e space w i l l space b e space u n i f o r m l y space c i r c u l a r space i f$

$I f space m space left parenthesis g plus pi n r squared right parenthesis space a n d space m left parenthesis g plus pi n r right parenthesis space r e p r e s e n t space r a d i a l space a n d space tan g e n t i a l space a c c e l e r a t i o n s comma space t h e space m o t i o n space o f space a space p a r t i c l e space w i l l space b e space u n i f o r m l y space c i r c u l a r space i f$

PhysicsMechanics

Mechanics

Physics

$W h i c h space o f space t h e space f o l l o w i n g space s t a t e m e n t s space i s space f a l s e space f o r space a space p a r t i c l e space m o v i n g space i n space a space c i r c l e space w i t h space a space c o n s tan t space a n g u l a r space s p e e d$

$W h i c h space o f space t h e space f o l l o w i n g space s t a t e m e n t s space i s space f a l s e space f o r space a space p a r t i c l e space m o v i n g space i n space a space c i r c l e space w i t h space a space c o n s tan t space a n g u l a r space s p e e d$

PhysicsMechanics

Mechanics

Physics

$W h e n space a space b o d y space m o v e s space i n space a space c i r c u l a r space p a t h comma space n o space w o r k space i s space d o n e space b y space t h e space f o r c e space sin c e comma$

$W h e n space a space b o d y space m o v e s space i n space a space c i r c u l a r space p a t h comma space n o space w o r k space i s space d o n e space b y space t h e space f o r c e space sin c e comma$

PhysicsMechanics

Mechanics

Physics

In uniform circular motion

In uniform circular motion

PhysicsMechanics

Mechanics

Physics

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

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

PhysicsMechanics

Mechanics

Physics

$A space p r o t o n space o f space m a s s space 1.6 space cross times space 10 to the power of negative 27 space end exponent k g space g o e s space r o u n d space i n space a space c i r c u l a r space o r b i t space o f space r a d i u s space 0.10 space m space u n d e r space a space c e n t r i p e t a l space f o r c e space o f space 4 space cross times space 10 to the power of negative 13 space space end exponent N. space space t h e n space t h e space f r e q u e n c y space o f space r e v o l u t i o n space o f space t h e space p r o t o n space i s space a b o u t$

$A space p r o t o n space o f space m a s s space 1.6 space cross times space 10 to the power of negative 27 space end exponent k g space g o e s space r o u n d space i n space a space c i r c u l a r space o r b i t space o f space r a d i u s space 0.10 space m space u n d e r space a space c e n t r i p e t a l space f o r c e space o f space 4 space cross times space 10 to the power of negative 13 space space end exponent N. space space t h e n space t h e space f r e q u e n c y space o f space r e v o l u t i o n space o f space t h e space p r o t o n space i s space a b o u t$

PhysicsMechanics

Mechanics

Physics

$A n space a t h l e t e space c o m p l e t e s space o n e space r o u n d space o f space a space c i r c u l a r space t r a c k space o f space r a d i u s space 10 space m space i n space 40 space s e c. space space T h e space d i s tan c e space c o v e r e d space b y space h i m space i n space 2 space m i n space 20 space s e c space i s$

$A n space a t h l e t e space c o m p l e t e s space o n e space r o u n d space o f space a space c i r c u l a r space t r a c k space o f space r a d i u s space 10 space m space i n space 40 space s e c. space space T h e space d i s tan c e space c o v e r e d space b y space h i m space i n space 2 space m i n space 20 space s e c space i s$

PhysicsMechanics

Mechanics

Physics

$T h e space c o e f f i c i e n t space o f space f r i c t i o n space b e t w e e n space t h e space t y r e s space a n d space t h e space r o a d space i s space 0.25. space space T h e space m a x i m u m space s p e e d space w i t h space w h i c h space a space c a r space c a n space b e space d r i v e n space r o u n d space a space c u r v e space o f space r a d i u s space 40 space m space w i t h o u t space s k i d d i n g space i s space left parenthesis a s s u m e open g equals 10 m s to the power of negative 2 end exponent close parentheses$

$T h e space c o e f f i c i e n t space o f space f r i c t i o n space b e t w e e n space t h e space t y r e s space a n d space t h e space r o a d space i s space 0.25. space space T h e space m a x i m u m space s p e e d space w i t h space w h i c h space a space c a r space c a n space b e space d r i v e n space r o u n d space a space c u r v e space o f space r a d i u s space 40 space m space w i t h o u t space s k i d d i n g space i s space left parenthesis a s s u m e open g equals 10 m s to the power of negative 2 end exponent close parentheses$

PhysicsMechanics

Mechanics

Physics

$A space m o t o r space c y c l e space d r i v e r space d o u b l e s space i t s space v e l o c i t y space w h e n space h e space i s space h a v i n g space a space t u r n. space space T h e space f o r c e space e x e r t e d space o u t w a r d l y space w i l l space b e$

$A space m o t o r space c y c l e space d r i v e r space d o u b l e s space i t s space v e l o c i t y space w h e n space h e space i s space h a v i n g space a space t u r n. space space T h e space f o r c e space e x e r t e d space o u t w a r d l y space w i l l space b e$

PhysicsMechanics

Mechanics

Physics

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

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

PhysicsMechanics

Mechanics

Physics

$T h e space m a x i m u m space v e l o c i t y space left parenthesis i n space m s – 1 right parenthesis space w i t h space w h i c h space a space c a r space d r i v e r space m u s t space t r a v e r s e space a space f l a t space c u r v e space o f space r a d i u s space 150 space m space a n d space c o e f f i c i e n t space o f space f r i c t i o n space 0.6 space t o space a v o i d space s k i d d i n g space i s space$
The maximum velocity (in ms^–1) with which a car driver must traverse a flat curve of radius 150 m and coefficient of friction 0.6 to avoid skidding is

$T h e space m a x i m u m space v e l o c i t y space left parenthesis i n space m s – 1 right parenthesis space w i t h space w h i c h space a space c a r space d r i v e r space m u s t space t r a v e r s e space a space f l a t space c u r v e space o f space r a d i u s space 150 space m space a n d space c o e f f i c i e n t space o f space f r i c t i o n space 0.6 space t o space a v o i d space s k i d d i n g space i s space$
The maximum velocity (in ms^–1) with which a car driver must traverse a flat curve of radius 150 m and coefficient of friction 0.6 to avoid skidding is

PhysicsMechanics

Mechanics

Physics

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

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

PhysicsMechanics

Mechanics

Physics

$I n space a n space a t o m space f o r space t h e space e l e c t r o n space t o space r e v o l v e space a r o u n d space t h e space n u c l e u s comma space t h e space n e c e s s a r y space c e n t r i p e t a l space space f o r c e space i s space o b t a i n e d space f r o m space t h e space f o l l o w i n g space f o r c e space e x e r t e d space b y space t h e space n u c l e u s space o n space t h e space e l e c t r o n$

$I n space a n space a t o m space f o r space t h e space e l e c t r o n space t o space r e v o l v e space a r o u n d space t h e space n u c l e u s comma space t h e space n e c e s s a r y space c e n t r i p e t a l space space f o r c e space i s space o b t a i n e d space f r o m space t h e space f o l l o w i n g space f o r c e space e x e r t e d space b y space t h e space n u c l e u s space o n space t h e space e l e c t r o n$

PhysicsMechanics

Mechanics

Physics

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

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

PhysicsMechanics

Mechanics

Physics

$A space s c o o t e r space i s space g o i n g space r o u n d space a space c i r c u l a r space r o a d space o f space r a d i u s space 100 space m space a t space a space s p e e d space o f space 10 space m divided by s. space space T h e space a n g u l a r space s p e e d space o f space t h e space s c o o t e r space w i l l space b e$

$A space s c o o t e r space i s space g o i n g space r o u n d space a space c i r c u l a r space r o a d space o f space r a d i u s space 100 space m space a t space a space s p e e d space o f space 10 space m divided by s. space space T h e space a n g u l a r space s p e e d space o f space t h e space s c o o t e r space w i l l space b e$

PhysicsMechanics

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