Consider a point object of mass 'm' moving in a circle of radiusa=1m. For anyinstantaneouspositionof theobject, theta is the angle that theradiallinejoiningtheobjectand thecentremakeswiththeposition X-axisof a cartesiancoordinatesystemwith thecentreof circle Oas theorigin. hati and hatj are unit vectors along X- axisand Y-axis, respectively . Suppose that the motion is a 'Unifrom Circular Motion ' with a constantangularspeed(pi)/(36) rad//sec and that thesense of rotationis counterclockwisewiththeta = 0 at t = 0 . For an object whichmovesin a circle , it isusuallyconvenientto introduce twomutuallyperpendicularunitvectors hatr_(r) and hatr_(t), as shown in thefig 3.57. Here hatr_(r)is theradialunit vectorand hatr_(t) , thetangential unitvector.Answerthe followingquestions : For anyinstantantaneousposition of theobjectedP, theradialunit vector hatr_(r)can be expressedas :

Consider a point object of mass 'm' moving in a circle of radiusa=1m.

1.	Consider a point object of mass 'm' moving in a circle of radiusa=1m. For anyinstantaneouspositionof theobject, theta is the angle that theradiallinejoiningtheobjectand thecentremakeswiththeposition X-axisof a cartesiancoordinatesystemwith thecentreof circle Oas theorigin. hati and hatj are unit vectors along X- axisand Y-axis, respectively . Suppose that the motion is a 'Unifrom Circular Motion ' with a constantangularspeed(pi)/(36) rad//sec and that thesense of rotationis counterclockwisewiththeta = 0 at t = 0 . For an object whichmovesin a circle , it isusuallyconvenientto introduce twomutuallyperpendicularunitvectors hatr_(r) and hatr_(t), as shown in thefig 3.57. Here hatr_(r)is theradialunit vectorand hatr_(t) , thetangential unitvector.Answerthe followingquestions : For anyinstantantaneousposition of theobjectedP, theradialunit vector hatr_(r)can be expressedas :
Answer» Solution : `vecr_(r) = HATI cos THETA + hatj SIN theta `