statics 3d equilibrium problems with angles

The rules stay the same: thumb towards z, curled fingers towards y, extended fingers towards x.

Now practice using the right hand rule if you are trying to find x. It’s important for you to be able to envision how the axes are perpendicular. Sometimes you will need to flip your hand 180 degrees to find which way lets you point your fingers in the y direction, for example: Using this x and y, let’s use the right-hand rule to find the direction of z. Imagine (or draw) the right-angle symbols (Answer will be in a few steps) Example 1: The hardest part of right-hand rule is imagining the different axes and envisioning how they are perpendicular to each other. Note that we are calculating the torque with respect to a point rather than an axis-the axis about which the torque acts, comes out in the answer. To determine the sense of rotation that such a torque vector would correspond to, about the axis defined by the torque vector itself, we use The Right Hand Rule For Something Curly Something Straight. When we use the cross product to calculate the torque due to a force F whose point of application has a position vector r, relative to the point about which we are calculating the torque, we get an axial torque vector τ. In the case at hand, it is straight out of the page. Hence, if you draw them so that both of the vectors that are in the cross product are in the plane of the page, the cross product vector will always be perpendicular to the page, either straight into the page, or straight out of the page. The cross product vector C is always perpendicular to both of the vectors that are in the cross product (the A and the B in the case at hand). Your thumb is now pointing in the direction of the cross product vector. Now rotate your hand, as necessary, about an imaginary axis extending along your forearm and along your middle finger, until your hand is oriented such that, if you were to close your fingers, they would point in the direction of the second vector. Keeping your fingers aligned with your forearm, point your fingers in the direction of the first vector (the one that appears before the “×” in the mathematical expression for the cross product e.g. To apply this right-hand rule, extend the fingers of your right hand so that they are pointing directly away from your right elbow.

The direction of the cross product vector A x B is given by the right-hand rule for the cross product of two vectors.

Statics 3d equilibrium problems with angles