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27 Nov 2019
(A) Show that the position of a particle on a circle of radius Rwith center at the origin (x=0,y=0) is given in unit vectors byr=cosθi+sinθj, where θ is the angle of the position vector with thex axis.
B) If the particle moves with constant speed v and period T,starting on the x axis at t=0, find an expression for θ in terms ofthe time and T.
C) Differentiate the position vector twice with respect to timeto find the acceleration and show that it is the centripetalacceleration, whose magnitude is given by equation (a=(v^2)/r) andwhose direction is toward the center of the circle. (Not that theunit vectors i and j are constants, independent of time.)
(A) Show that the position of a particle on a circle of radius Rwith center at the origin (x=0,y=0) is given in unit vectors byr=cosθi+sinθj, where θ is the angle of the position vector with thex axis.
B) If the particle moves with constant speed v and period T,starting on the x axis at t=0, find an expression for θ in terms ofthe time and T.
C) Differentiate the position vector twice with respect to timeto find the acceleration and show that it is the centripetalacceleration, whose magnitude is given by equation (a=(v^2)/r) andwhose direction is toward the center of the circle. (Not that theunit vectors i and j are constants, independent of time.)
Hubert KochLv2
16 Apr 2019
