The position of a particle is given i(t) = A(coswt i + sin wt 1), where w is a constant. (a) Show that the particle moves in a circle of radius A. (b) Calculate and then show that the speed of the particle is a constanta (c) Determine and show that a is given by ae = rw?. (d) Calculate the centripetal force on the particle.

Explanation:

(a) we can prove that the particle moves in a circle by taking the square of the norm of r(t)

the norm of the position vector does not depend of time, so |r| is constant and is a radius of a circle.

(b) the sped of the particle is the norm of the velocity v(t). Velocity is calculated by derivating r(t)

A and w are constant, hence the speed of the particle is constant.

(c) the acceleration is the derivative of the velocity

(d)

I hope this is useful for you

regards

the tires are rotating at 0.434 rpmlinear speed=45 m/sdiameter=0.550 mradius=0.275 mnow v= rωω= v/rω=45/0.275ω=163.6 rad/sω=163.6 rad/s (1rev/2π rad) (60s/1m)ω=1563 rpm