This paper first proves several fractional forms of the kinetic energy theorem for particles in Cartesian and cylindrical coordinate systems, termed the kinetic energy theorem equations for translational and rotational motions, along with orthogonal superposition rules for work. Then, applying the knowledge of conservation of axial momentum moment, a conventional solution for the 11th question of the 2024 Jiangsu Provincial Physics College Entrance Examination is given, and a trend chart of the angle θ changing with the length l of the diagonal rope both in the question's diagram is made. Finally, by applying the so-called formula for the kinetic energy theorem of component motion that has been proven in the cylindrical coordinate system, it is gradually inferred approximately within the scope of middle school physics knowledge that options (B), (A), and (D) of the question are all incorrect. The content of the paper can provide useful supplements for mechanics related content in universities, as well as reference for physics teaching in universities and middle schools.

This paper first introduces the origin of “rolling friction force”. Then, it provides a more accurate dynamic equation for a starting car. Furthermore, the acceleration motion of an ordinary car starting at a constant effective power is calculated to obtain a relatively realistic image of the speed changing over time. At the same time, it provides necessary explanations for some key aspects and offers several insights for related basic physics teaching. At the end of the article, some necessary explanations are provided too, and it is pointed out that this paper still belongs to the theoretical model research under a constant effective output power in essence. The main purpose of this paper is to provide a more realistic motion image and to clarify some understandings for reference.

This paper derives the accurate velocity of the center of the shading strip passing through two photoelectric gates in the experiment to verify Newton's second law, and the strict result of the slider's acceleration is also deduced. The analysis shows that these strictly accurate results are almost indistinguishable in magnitude from the measurement results obtained in common experiments where average velocity is used instead of instantaneous velocity, that is, the systematic error brought by the usual practice in experiments is almost zero. However, in terms of qualitative nature, the measured velocity is slightly less than its accurate value, while the measured acceleration is slightly greater than its accurate value. To enrich the content, this paper further infers the relative error of the measured acceleration expressed by the width of the light-blocking strip and its two segments of displacement, and judges the trend of the relative error with the changes of various parameters based on this. Although this paper is essentially a theoretical study and has little reference value for actual experiments, its theoretical reference value objectively exists, and it should be of some help for the teaching of related content in universities and middle schools as well as the cultivation of scientific literacy.

This paper first analyzes preliminarily the causes of the real image and virtual image formed by the reflection of convex lens double spherical surface, and measures the image distance of the real image through the experiment. Then, the focal length formula of biconvex thick lens is deduced by using the basic knowledge of geometric optics. Combined with the measured data, the refractive index of the convex lens is calculated to be 1.50, and then the theoretical image distance of the object point on the optical axis reflected into a real image and a virtual image by the double spherical surface is calculated step by step. Then, the non paraxial imaging simulation is carried out by using analytic geometry knowledge and Excel software, following the law of light reflection and refraction.Finally, the paraxial theoretical results, non-paraxial simulation results and experimental results are compared to find out the gap. On the basis of exploring the causes for the gap, the article attempts to explain some related phenomena and provide some research implications.

Firstly, it is proved that it is completely feasible to take the air resistance coefficient C_D as 0.42 for the vertical upward throwing motion of a small solid ball with usual material, size and initial velocity (non high speed) in the air. The air resistance is regarded as the quadratic function of speed in this paper, and the traditional research idea is adopted to gradually deduce the kinematic equation of the non high speed vertical throwing motion of an ordinary small ball in the air, and then deduce the rising time and maximum height of the small ball, as well as the falling time and landing speed. The results show that the rising time of the small ball is less than the falling time, while the latter is less than the rising or falling time without air resistance. At the same initial velocity, the motion of a homogeneous solid bigger ball is less affected by air resistance. When the initial velocity is the same and the product of density and radius is the same, the solid balls with different materials and sizes have the same upward throwing motion. Taking a small solid iron ball with a radius of 1 cm as an example, the variation curves of various motion characteristic parameters with initial velocity and the variation curves of small ball displacement with time under several different initial velocities are calculated and made. The results show that the larger the initial velocity is, the more the motion of the ball deviates from the ideal situation without air resistance. At the end of the paper, some possible interference or error factors are briefly summarized.