Flag Mechanics> rotational dynamics...
question mark

The magnitude of displacement of a particle moving in a circle of radius 'a' with constant angular speed 'w' varies with time 't' as:

bhanuveer danduboyina , 14 Years ago
Grade 12th Pass
anser 2 Answers
vikas askiitian expert

Last Activity: 14 Years ago

R = acos@ (i) + asin@ (j)       ................1        

R is the position vector of particle at any time performing circular motion...

@ is angular displacement

 

w = @/t

@ = wt         ..............2

from 1 & 2

Rt = acoswt (i) + asinwt (j)          .............3

at t = 0 ,

Ro = a (i)             ..............4

 

displacement = Rt - Ro = a(coswt-1) (i) + a(sinwt) (j)

magnitude =[ (a2(coswt-1)2 + a2(sinwt)2]1/2

                =  [2a2 - 2a2coswt]1/2

                = a[2(1-coswt)]1/2

 

now , coswt = (1-2cos2(wt/2)) , after putting this in above eq

  magnitude = 2a[cos2(wt/2)]1/2

                  =2acos(wt/2)

this is the required result ,

 

approve if u like my ans

akvstr18

Last Activity: 6 Years ago

in the above answer it sayscoswt=1-cos^2(wt/2)but coswt = 1-sin^2(wt/2)=cos^2 (wt/2)-1also 2^(1/2) is not considered the final magnitude will be: (2)^(1/2)asin (wt/2)

Provide a better Answer & Earn Cool Goodies

star
LIVE ONLINE CLASSES

Prepraring for the competition made easy just by live online class.

tv

Full Live Access

material

Study Material

removal

Live Doubts Solving

assignment

Daily Class Assignments


Ask a Doubt

Get your questions answered by the expert for free