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Physics

Mechanics

Easy

Question

The moment of inertia of an angular wheel shown in figure is 3200 kgm². If the inner radius is 5 cm and the outer radius is 20cm, and the wheel is acted upon by the forces shown, then the angular acceleration of the wheel is

$10^{- 1} rad / s^{2}$
$10^{- 2} rad / s^{2}$
$10^{- 3} rad / s^{2}$
$10^{- 4} rad / s^{2}$

The correct answer is: $10 to the power of negative 3 end exponent rad divided by straight s squared$

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A beam of length $l$ lies on the +x axis with its left end on the origin. A cable pulls the beam in y-direction with a force $straight F equals straight F subscript 0 left parenthesis 1 minus straight x over ell right parenthesis$ .If the axis is fixed at x = 0 then find the torque

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$T w o space p a r t i c l e s space A space a n d space B space a r e space s i t u a t e d space a t space a space d i s tan c e space d equals 2 space m space a p a r t. space P a r t i c l e space A space h a s space a space v e l o c i t y space o f space 10 space m space divided by space s space a t space a n space a n g l e space o f space 60 to the power of 0 space a n d space p a r t i c l e space B space h a s space a space v e l o c i t y space v space a t space a n space a n g l e 30 to the power of 0 space a s space s h o w n space i n space f i g u r e. space T h e space d i s tan c e space d space b e t w e e n space A space a n d space B space i s space c o n s tan t. space T h e space a n g u l a r space v e l o c i t y space o f space B space w i t h space r e s p e c t space t o space A space i s colon$

PhysicsMechanics

$A space h o o p space r o l l s space o n space a space h o r i z o n t a l space g r o u n d space w i t h o u t space s l i p p i n g space w i t h space l i n e a r space s p e e d space v. space S p e e d space o f space a space p a r t i c l e space P space o n space t h e space c i r c u m f e r e n c e space o f space t h e space h o o p space a t space a n g l e space theta space i s colon$

$A space h o o p space r o l l s space o n space a space h o r i z o n t a l space g r o u n d space w i t h o u t space s l i p p i n g space w i t h space l i n e a r space s p e e d space v. space S p e e d space o f space a space p a r t i c l e space P space o n space t h e space c i r c u m f e r e n c e space o f space t h e space h o o p space a t space a n g l e space theta space i s colon$

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

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PhysicsMechanics

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