OSAT Physics (114)

An object at rest remains at rest, and an object in motion continues in motion with constant velocity, unless acted upon by a net external force. This property of matter to resist changes in motion is called inertia. Mass is the quantitative measure of inertia.

An inertial reference frame is one in which Newton's first law holds. Any reference frame moving at constant velocity relative to an inertial frame is also inertial. Accelerating reference frames are non-inertial, and fictitious forces appear in such frames.

The net force on an object equals the product of its mass and acceleration:

ΣF = ma

For rotational motion, the analogous relationship is:

Στ = Iα

where τ is torque, I is moment of inertia, and α is angular acceleration.

For every action force, there exists an equal and opposite reaction force. These forces act on different objects and never cancel each other. When object A exerts a force on object B, object B simultaneously exerts a force of equal magnitude but opposite direction on object A.

Action-reaction pairs have identical magnitudes regardless of the masses involved. A bug hitting a windshield experiences the same magnitude of force as the windshield experiences from the bug; however, the acceleration differs due to different masses.

Problem-solving with Newton's laws requires systematic application of free-body diagrams. Identify the object of interest, draw all forces acting on that object, choose a coordinate system, resolve forces into components, apply Newton's second law in each direction, and solve the resulting equations.

For objects in equilibrium (acceleration equals zero), the net force in each direction equals zero. For accelerating objects, set up equations where net force equals mass times acceleration.

Weight is the gravitational force exerted on an object by a planet or other massive body. Near Earth's surface, W = mg, where g ≈ 9.8 m/s². Weight is a force measured in newtons, distinct from mass measured in kilograms.

The normal force is a contact force perpendicular to a surface. It adjusts to prevent objects from passing through surfaces. On a horizontal surface with no other vertical forces, the normal force equals the weight. On an incline at angle θ, the normal force equals mg cos θ.

Friction opposes relative motion or attempted motion between surfaces in contact. Static friction prevents motion and can range from zero up to a maximum value: f_s ≤ μ_s N, where μ_s is the coefficient of static friction and N is the normal force.

Kinetic friction acts on moving objects and has constant magnitude: f_k = μ_k N. The kinetic coefficient is typically less than the static coefficient for the same surfaces. Friction depends on surface properties and normal force but is independent of contact area and sliding speed.

Tension is the pulling force transmitted through a rope, string, or cable. In an ideal massless rope, tension is the same throughout. When a rope passes over a frictionless pulley, it redirects the tension force without changing its magnitude.

For systems with multiple objects connected by ropes, tension provides the force that accelerates connected objects together. Analyze each object separately with its own free-body diagram, using the same tension magnitude and the same acceleration for objects connected by inextensible ropes.

An ideal spring obeys Hooke's Law: F = -kx, where k is the spring constant (stiffness) and x is the displacement from equilibrium. The negative sign indicates that the spring force opposes displacement. Springs stretched beyond equilibrium pull back; springs compressed below equilibrium push out.

Spring constants are measured in N/m. A larger spring constant means a stiffer spring requiring more force for the same displacement. Springs in series have an effective constant given by 1/k_eff = 1/k₁ + 1/k₂. Springs in parallel have k_eff = k₁ + k₂.

Newton's Law of Universal Gravitation states that every mass attracts every other mass with a force proportional to the product of their masses and inversely proportional to the square of the distance between their centers:

F = Gm₁m₂/r²

where G = 6.67 × 10⁻¹¹ N·m²/kg² is the universal gravitational constant.

Surface gravity on a planet of mass M and radius R is g = GM/R². Orbital motion results when gravitational force provides the centripetal force needed for circular motion. For circular orbits, v = √(GM/r) and T = 2π√(r³/GM).

On an incline at angle θ, decompose the weight into components parallel and perpendicular to the surface. The component parallel to the incline is mg sin θ, causing acceleration down the slope if no other forces act. The perpendicular component is mg cos θ, which the normal force balances.

With friction on an incline, the friction force acts parallel to the surface opposing motion. For an object sliding down, friction acts upward along the incline. For an object being pushed up, friction acts downward along the incline.

For uniform circular motion, the net force must point toward the center of the circle (centripetal force). This is not a new type of force but rather the net effect of real forces such as tension, gravity, friction, or normal force.

F_c = mv²/r = mω²r

For a car on a banked curve, the horizontal component of the normal force provides centripetal force. The ideal banking angle θ for speed v and radius r satisfies tan θ = v²/rg.