Final answer:
The direction of chip flow in relation to tool geometry when turning a steel rod on a lathe cannot be determined without additional specifics about the tool. The angular velocity of a piece of wood on a lathe when a chisel is applied depends on the lathe's ability to compensate for the exerted force. Finally, angular acceleration of a grindstone pressed by a steel axe involves calculations involving friction and the moment of inertia.
Step-by-step explanation:
Concepts of Turning a Steel Rod and Angular Velocity
When turning a steel rod on a lathe, the chip flow direction depends on multiple factors including the tool geometry and cutting conditions. However, the provided question does not specify sufficient details for a calculation. The deviation from the orthogonal plane cannot be determined without additional information such as tool cutting angle, rake angle, and the approach angle.
Assuming the second part of the question refers to the overall concept of maintaining angular velocity in lathe operations, holding a chisel to a spinning wood does not inherently change the angular velocity of the object. The angular velocity of a lathe remains constant unless the motor speed is adjusted or an external force (e.g., friction, cutting force) acts opposite to the rotation. The force exerted by the chisel would create a torque that may affect the angular velocity depending on the resistance provided by the lathe and the moment of inertia of the object being turned. Typically, the motor compensates to maintain a steady angular velocity unless the force exceeds the motor's capacity.
For the last scenario, with the grindstone and the steel axe: the angular acceleration can be calculated using the friction force that arises from the applied radial force and the kinetic coefficient of friction. The moment of inertia must be considered to find the angular acceleration, and knowing the initial angular velocity and acceleration, one can calculate how many turns the stone will make before stopping, using rotational kinematics.
The scenario with the uniform rod and beads sliding outward exemplifies the conservation of angular momentum, where the angular velocity decreases as the mass distribution changes (beads move outward) due to the increase in moment of inertia.
The analysis of moments, stresses, and deflections in mechanical design such as determining the needed diameter of a steel rod to support a truck without unacceptable stretching involves principles of material mechanics and strength of materials.