Example Sliding ba Consider a bar leaning against the wall and slipping downward. It is clear that while the bar is in contact with the wall and the foor, the velocity at point P will be in the vertical direction, whereas the velocity at point P will be in the horizontal direction. Therefore, drawing the perpendicular lines to up and upr throug ts p and P. we can determine the instantaneous center of rotation c It should be noted that, for a general motion, the location of the center of rotation will change in time. The path described by the instantaneous center of rotation is called the space centrode, and the locus of he positions of the instantaneous centers on the body is called the body centrode. At a given instant, the pace centrode and the body centrode curves are tangent. The tangency point is precisely the instantaneous center of rotation, C. It is not difficult to show that, for the above example, the space and body centrode are circular arcs, assuming that the points P and P remain in contact with the walls at all times(as you will see in the homework problem, this requires some friction) body centrode space centrode From this example, it should be clear that although we think about the instantaneous center of rotation as a point attached to the body, it need not be a material point. In fact, it can be a point" outside"the body It is also possible to consider the instantaneous center of acceleration as the point at which the instantaneous acceleration is zero Example Rolling Cylinder Consider a cylinder rolling on a fat surface, without sliding, with angular velocity w and angular acceleration a. We want to determine the velocity and acceleration of point P on the cylinder. In order to illustrate the various procedures described, we will consider three different approachesExample Sliding bar Consider a bar leaning against the wall and slipping downward. It is clear that while the bar is in contact with the wall and the floor, the velocity at point P will be in the vertical direction, whereas the velocity at point P ′ will be in the horizontal direction. Therefore, drawing the perpendicular lines to vP and vP ′ through points P and P ′ , we can determine the instantaneous center of rotation C. It should be noted that, for a general motion, the location of the center of rotation will change in time. The path described by the instantaneous center of rotation is called the space centrode, and the locus of the positions of the instantaneous centers on the body is called the body centrode. At a given instant, the space centrode and the body centrode curves are tangent. The tangency point is precisely the instantaneous center of rotation, C. It is not difficult to show that, for the above example, the space and body centrodes are circular arcs, assuming that the points P and P ′ remain in contact with the walls at all times (as you will see in the homework problem, this requires some friction). space centrode body centrode From this example, it should be clear that although we think about the instantaneous center of rotation as a point attached to the body, it need not be a material point. In fact, it can be a point “outside” the body. It is also possible to consider the instantaneous center of acceleration as the point at which the instantaneous acceleration is zero. Example Rolling Cylinder Consider a cylinder rolling on a flat surface, without sliding, with angular velocity ω and angular acceleration α. We want to determine the velocity and acceleration of point P on the cylinder. In order to illustrate the various procedures described, we will consider three different approaches. 5