A Square Box with No Fixed Axis Acted On By Three Horizontal Forces
In the figure below, the mass of the square box is 21.0 kg . All of the horizontal forces acting on the box are shown in the figure.
Each of the figures below shows a top view of an object on a frictionless surface. Information about the motion of the object may or may not be given; but in all cases, if the object is moving, it is moving with no friction in the horizontal plane. Each figure will be drawn at a particular instant of time, and will show either all of the horizontal forces acting on the object, or else all of the horizontal forces except one; the vertical forces acting on the object, weight and normal force, always add to zero. For each figure, towards the top of the page is North and to the right on the page is East. In each case, the questions refer to the particular instant of time for which the figure is drawn.
The grid squares in each figure give a scale for both force and distance. For forces, the width of each square represents 0.450 N , and for distances, the width of each square represents 12.0 cm . The density of each object is uniform, making the center-of-mass location for each object easy to determine.
1. For this box, at this instant of time, what is the angular acceleration of the box about a vertical axis through its center of mass? HINT: use the second law for rotation about the specified center-of-mass axis. For the direction, let a counterclockwise angular acceleration be positive.
2. For this box, at this instant of time, what is the acceleration of its center of mass? If the acceleration is zero, put zero for the angle when expressing the direction.
In the figure below, the mass of the stick is 450.0 grams . The stick is very thin, so you may ignore the width of the stick. All of the horizontal forces acting on the stick are shown in the figure.
3. For this stick, at this instant of time, what is the angular acceleration of the stick about a vertical axis through its center of mass? For the direction, let counterclockwise be positive.
4.For this stick, at this instant of time, what is the acceleration of its center of mass? If the acceleration is zero, put zero for the angle when expressing the direction.