Question

3. A circular disk of radius 2 cm slides at a speed 10 cm/sec in the direction of (t) (3, 4). As it slides it spins counterclockwise at 3 revolutions per second. Initially (ie, t = 0), the center of the disk is at the origin, O- (0,0). Find parametric equations for the trajectory of the point P on the edge of the disk, which is initially at (2,0). (Hint: Split the motion into sliding(i.e. translation) of the center and rotation about the center. Use vector addition(i.e. position vector) OP for parametrization.)

Answer 1

A circular disk of radius 2cm slides at a speed of 10 cm/sec in the direction of r^rightarrow (t) = < 3, 4). As it slides it spins counterclockwise at 3 revolutions per second. Initially (i.e. , t = 0) the center of the disk is at the origin. O = (0, 0). Find parametric equation for the trajectory of the point p on the edge of the disk, which is initially at (2, 0). The unit of vector in the direction of r^rightarrow (t) = < 3, 4 > is < 3/5, 4/5 > we will to parameterized the curve by time t in seconds. To do this we split the motion into translation of the center and rotation about the center. And use vectors to do the analysis. At the time the center has moved to C. Thus, OC^rightarrow = 10t < 3/5, 4/5 > = <