Tangent acceleration is the acceleration of an object in the direction of its motion, while normal acceleration is the acceleration perpendicular to the direction of motion. In other words, tangent acceleration affects the speed of the object, while normal acceleration affects the direction of motion.
The curvature radius of a curve is calculated by taking the reciprocal of the curvature at a specific point on the curve. The curvature can be found by dividing the absolute value of the second derivative of the curve by the cube of the first derivative at that point.
The curvature of a curve is inversely proportional to the curvature radius. This means that as the curvature radius increases, the curvature decreases and vice versa.
Tangent acceleration changes the speed of an object, while normal acceleration changes the direction of motion. When an object experiences both tangential and normal acceleration, its motion will be curved. The direction of the object's motion will also constantly change due to the normal acceleration.
No, the curvature radius cannot be negative. It is always a positive value, as it is calculated by taking the reciprocal of the curvature, which is also always positive. A negative curvature radius would imply that the curvature is also negative, which is not possible for a physical curve.