IBDP Physics 2025 SL&HL: 2.3 Newton’s second law in terms of momentum Study Notes

Learning Objectives

Students should understand
• Newton’s three laws of motion
• forces as interactions between bodies
• that forces acting on a body can be represented in a free-body diagram
• that free-body diagrams can be analysed to find the resultant force on a system
• the nature and use of the following contact forces

◦ normal force F_N is the component of the contact force acting perpendicular to the surface that counteracts the body
◦ surface frictional force F_f acting in a direction parallel to the plane of contact between a body and a surface, on a stationary body as given by F_f ≤ μ_sF_N or a body in motion as given by F_f = μ_dF_N where μs and μd are the coefficients of static and dynamic friction respectively
◦ tension
◦ elastic restoring force F_H following Hooke’s law as given by F_H = –kx where k is the spring constant
◦ viscous drag force F_d acting on a small sphere opposing its motion through a fluid as given by F_d = 6πηrv where η is the fluid viscosity, r is the radius of the sphere and v is the velocity of the sphere through the fluid
◦ buoyancy F_b acting on a body due to the displacement of the fluid as given by F_b = ρVg where V is the volume of fluid displaced

• the nature and use of the following field forces

◦ gravitational force F_g is the weight of the body and calculated is given by F_g = mg
◦ electric force Fe
◦ magnetic force F_m

• that linear momentum as given by p = mv remains constant unless the system is acted upon by a resultant external force
• that a resultant external force applied to a system constitutes an impulse J as given by J = FΔt where F is the average resultant force and Δt is the time of contact
• that the applied external impulse equals the change in momentum of the system
• that Newton’s second law in the form F = ma assumes mass is constant where as F = Δp Δt allows for situations where mass is changing
• the elastic and inelastic collisions of two bodies
• explosions
• energy considerations in elastic collisions, inelastic collisions, and explosions
• that bodies moving along a circular trajectory at a constant speed experience an acceleration that is directed radially towards the centre of the circle—known as a centripetal acceleration as given by
       \(a=\frac{v^2}{r}=\omega^2r=\frac{4\pi^2r}{T^2}\)
• that circular motion is caused by a centripetal force acting perpendicular to the velocity
• that a centripetal force causes the body to change direction even if its magnitude of velocity may remain constant
• that the motion along a circular trajectory can be described in terms of the angular velocity ω which is related to the linear speed v by the equation as given by

    \(v=\frac{2\pi r}{T}=\omega r\)