Elementary Plane Rigid Dynamics by H. W. Harkness

By H. W. Harkness

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The remaining forces — P and F constitute a couple acting on the body to give it rotation. Since they have equal and opposite effects upon the translation of the center of mass it follows that the rotation must be round the center of mass. 48 II. GENERAL PLANE MOTION OF A RIGID BODY A. M. Worthington has given a good demonstration to illustrate the point that a couple acting upon a body free to move will give the body rotational motion round the center of mass. A magnet SN is fixed to a cork C and the whole floated in water the weight W serving to float the cork evenly in the water.

00 sec -1 . 600 (53°8/), with the vertical calculate the acceleration of the wheel around A, the point of contact of the wheel with the surface, the friction which is acting between the wheel face and the surface and the normal reaction of the surface with the wheel. From the geometry of the figure So angle OGA is 90° and 56 II. 600 K Since the wheel does not slip, the horizontal component of the acceleration of A is zero. So this component of the inertial force at A is also zero. Diagram II-3 shows the acceleration components at A and G.

Writing the torque round an axis through the instantaneous center we have (see Figure 1-17) FIG. )]. It will be noted that the friction acting at A does no work unless slipping occurs. T h e friction merely prevents the two surfaces from slipping one upon the other. T h e friction has an effect upon the acceleration of the body but this method of analysis has avoided that. This has a great advantage because since in this problem slipping does not occur the friction is, in general, not known in the first place.

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