A particle P moves with a constant speed v around the circular path of radius r. Start with the expression r=rr1 for the position vector of P and derive the expressions for the velocity v and acceleration a of P. The radial and transvers unit vectors are r1 and theta1 respectively.
so I know that with cartesian coordinates the position equation would be
rcos(theta)i+rsin(theta)j but after that I'm a little bit stuck. The teacher made some comment about recognizing that theta is dependent on time.
In two dimensions the position vector which has magnitude (length) and directed at an angle above the x-axis can be expressed in Cartesian coordinates using the unit vectors and :
Assume uniform circular motion, which requires three things.
Now find the velocity and acceleration of the motion by taking derivatives of position with respect to time.
Notice that the term in parenthesis is the original expression of in Cartesian coordinates. Consequently,
The negative shows that the acceleration is pointed towards the center of the circle (opposite the radius), hence it is called "centripetal" (i.e. "center-seeking"). While objects naturally follow a straight path (due to inertia), this centripetal acceleration describes the circular motion path caused by a centripetal force.