Final answer:
Computing true angles for cutting and forming tools involves using geometric principles and trigonometric relationships, often requiring a protractor for simple measurements or trigonometric functions for complex calculations.
Step-by-step explanation:
Computing the true angles for cutting and forming tools often involves a combination of geometric principles and trigonometric relationships. For instance, when looking to get the direction of the resultant force acting on a tool, you can measure the angle it makes with the reference frame using a protractor.
However, for more accurate and complex calculations, trigonometry is essential. The angles between tool edges and the workpiece or the angles involving the cutting forces can be determined using trigonometric functions such as sine, cosine, and tangent when dealing with right-angle triangles formed by these forces.
In the context of a grindstone, as in the case of pressing an axe against it, the angular acceleration can be calculated using the known kinetic coefficient of friction and force. Another example is when you fold paper to make a gnomon in constructing a sundial, ensuring that angles are measured correctly for accurate sundial function.
Moreover, the angular velocity of a piece of wood on a lathe and the calculation of centripetal acceleration and linear speed of a grindstone at its edge are examples that require an understanding of circular motion and the forces involved in cutting tools.