力与平动动力学

• 2.1.A.1 System properties are determined by the interactions between objects within the system.
• 2.1.A.2 If the properties or interactions of the constituent objects within a system are not important in modeling the behavior of the macroscopic system, the system can itself be treated as a single object.
• 2.1.A.3 Systems may allow interactions between constituent parts of the system and the environment, which may result in the transfer of energy or mass.
• 2.1.A.4 Individual objects within a chosen system may behave differently from each other as well as from the system as a whole.
• 2.1.A.5 The internal structure of a system affects the analysis of that system.
• 2.1.A.6 As variables external to a system are changed, the system's substructure may change.

• 2.1.B.1 For systems with symmetrical mass distributions, the center of mass is located on lines of symmetry.
• 2.1.B.2 The location of a system's center of mass along a given axis can be calculated using the equation
  • Equation: $\vec{x}_{cm} = \dfrac{\sum m_i \vec{x}_i}{\sum m_i}$
• 2.1.B.3 A system can be modeled as a singular object that is located at the system's center of mass.

Boundary statement: AP Physics 1 only expects students to calculate the center of mass for systems of five or fewer particles arranged in a two-dimensional configuration or for systems that are highly symmetrical.

• 2.2.A.1 Forces are vector quantities that describe the interactions between objects or systems.
  • 2.2.A.1.i A force exerted on an object or system is always due to the interaction of that object with another object or system.
  • 2.2.A.1.ii An object or system cannot exert a net force on itself.
• 2.2.A.2 Contact forces describe the interaction of an object or system touching another object or system and are macroscopic effects of interatomic electric forces.

• 2.2.B.1 Free-body diagrams are useful tools for visualizing forces being exerted on a single object or system and for determining the equations that represent a physical situation.
• 2.2.B.2 The free-body diagram of an object or system shows each of the forces exerted on the object by the environment.
• 2.2.B.3 Forces exerted on an object or system are represented as vectors originating from the representation of the center of mass, such as a dot. A system is treated as though all of its mass is located at the center of mass.
• 2.2.B.4 A coordinate system with one axis parallel to the direction of acceleration of the object or system simplifies the translation from free-body diagram to algebraic representation. For example, in a free-body diagram of an object on an inclined plane, it is useful to set one axis parallel to the surface of the incline.

Boundary statement: AP Physics 1 only expects students to depict the forces exerted on objects, not the force components on free-body diagrams. On the AP Physics exams, individual forces represented on a free-body diagram must be drawn as individual straight arrows, originating on the dot and pointing in the direction of the force. Individual forces that are in the same direction must be drawn side by side, not overlapping.

• 2.3.A.1 Newton's third law describes the interaction of two objects in terms of the paired forces that each exerts on the other.
  • Equation: $\vec{F}_{\text{A on B}} = -\vec{F}_{\text{B on A}}$
• 2.3.A.2 Interactions between objects within a system (internal forces) do not influence the motion of a system's center of mass.
• 2.3.A.3 Tension is the macroscopic net result of forces that segments of a string, cable, chain, or similar system exert on each other in response to an external force.
  • 2.3.A.3.i An ideal string has negligible mass and does not stretch when under tension.
  • 2.3.A.3.ii The tension in an ideal string is the same at all points within the string.
  • 2.3.A.3.iii In a string with nonnegligible mass, tension may not be the same at all points within the string.
  • 2.3.A.3.iv An ideal pulley is a pulley that has negligible mass and rotates about an axle through its center of mass with negligible friction.

Boundary statement: AP Physics 1 only expects students to describe tension qualitatively in a string, cable, chain, or similar system with mass. For example, students might note that the tension in a hanging chain is greater toward the top of the chain.

Boundary statement: The interaction between objects or systems at a distance is limited to gravitational forces in AP Physics 1. In AP Physics 2, gravitational, electric, and magnetic forces may be considered.

• 2.4.A.1 The net force on a system is the vector sum of all forces exerted on the system.
• 2.4.A.2 Translational equilibrium is a configuration of forces such that the net force exerted on a system is zero.
  • Derived equation: $\sum_i \vec{F}_i = 0$
• 2.4.A.3 Newton's first law states that if the net force exerted on a system is zero, the velocity of that system will remain constant.
• 2.4.A.4 Forces may be balanced in one dimension but unbalanced in another. The system's velocity will change only in the direction of the unbalanced force.
• 2.4.A.5 An inertial reference frame is one from which an observer would verify Newton's first law of motion.

• 2.5.A.1 Unbalanced forces are a configuration of forces such that the net force exerted on a system is not equal to zero.
• 2.5.A.2 Newton's second law of motion states that the acceleration of a system's center of mass has a magnitude proportional to the magnitude of the net force exerted on the system and is in the same direction as that net force.
  • Equation: $\vec{a}_{\text{sys}} = \dfrac{\sum \vec{F}}{m_{\text{sys}}} = \dfrac{\vec{F}_{\text{net}}}{m_{\text{sys}}}$
• 2.5.A.3 The velocity of a system's center of mass will only change if a nonzero net external force is exerted on that system.

• 2.6.A.1 Newton's law of universal gravitation describes the gravitational force between two objects or systems as directly proportional to each of their masses and inversely proportional to the square of the distance between the systems' centers of mass.
  • Equation: $\left|\vec{F}_g\right| = G\dfrac{m_1 m_2}{r^2}$
  • 2.6.A.1.i The gravitational force is attractive.
  • 2.6.A.1.ii The gravitational force is always exerted along the line connecting the centers of mass of the two interacting systems.
  • 2.6.A.1.iii The gravitational force on a system can be considered to be exerted on the system's center of mass.
• 2.6.A.2 A field models the effects of a noncontact force exerted on an object at various positions in space.
  • 2.6.A.2.i The magnitude of the gravitational field created by a system of mass $M$ at a point in space is equal to the ratio of the gravitational force exerted by the system on a test object of mass $m$ to the mass of the test object.
    • Equation: $\left|\vec{g}\right| = \dfrac{\left|\vec{F}_g\right|}{m} = G\dfrac{M}{r^2}$
  • 2.6.A.2.ii If the gravitational force is the only force exerted on an object, the observed acceleration of the object (in m/s$^2$) is numerically equal to the magnitude of the gravitational field strength (in N/kg) at that location.
• 2.6.A.3 The gravitational force exerted by an astronomical body on a relatively small nearby object is called weight.
  • Equation: $\text{Weight} = F_g = mg$

• 2.6.B.1 If the gravitational force between two systems' centers of mass has a negligible change as the relative position of the two systems changes, the gravitational force can be considered constant at all points between the initial and final positions of the systems.
• 2.6.B.2 Near the surface of Earth, the strength of the gravitational field is $g \approx 10 \text{ N/kg}$

• 2.6.C.1 The magnitude of the apparent weight of a system is the magnitude of the normal force exerted on the system.
• 2.6.C.2 If the system is accelerating, the apparent weight of the system is not equal to the magnitude of the gravitational force exerted on the system.
• 2.6.C.3 A system appears weightless when there are no forces exerted on the system or when the force of gravity is the only force exerted on the system.
• 2.6.C.4 The equivalence principle states that an observer in a noninertial reference frame is unable to distinguish between an object's apparent weight and the gravitational force exerted on the object by a gravitational field.

• 2.6.D.1 Objects have inertial mass, or inertia, a property that determines how much an object's motion resists changes when interacting with another object.
• 2.6.D.2 Gravitational mass is related to the force of attraction between two systems with mass.
• 2.6.D.3 Inertial mass and gravitational mass have been experimentally verified to be equivalent.

• 2.7.A.1 Kinetic friction occurs when two surfaces in contact move relative to each other.
  • 2.7.A.1.i The kinetic friction force is exerted in a direction opposite to the motion of each surface relative to the other surface.
  • 2.7.A.1.ii The force of friction between two surfaces does not depend on the size of the surface area of contact.
• 2.7.A.2 The magnitude of the kinetic friction force exerted on an object is the product of the normal force the surface exerts on the object and the coefficient of kinetic friction.
  • Equation: $\left|\vec{F}_{f,k}\right| = \left|\mu_k \vec{F}_n\right|$
  • 2.7.A.2.i The coefficient of kinetic friction depends on the material properties of the surfaces that are in contact.
  • 2.7.A.2.ii Normal force is the perpendicular component of the force exerted on an object by the surface with which it is in contact; it is directed away from the surface.

• 2.7.B.1 Static friction may occur between the contacting surfaces of two objects that are not moving relative to each other.
• 2.7.B.2 Static friction adopts the value and direction required to prevent an object from slipping or sliding on a surface.
  • Equation: $\left|\vec{F}_{f,s}\right| \leq \left|\mu_s \vec{F}_n\right|$
  • 2.7.B.2.i Slipping and sliding refer to situations in which two surfaces are moving relative to each other.
  • 2.7.B.2.ii There exists a maximum value for which static friction will prevent an object from slipping on a given surface.
    • Equation: $F_{f,s,\max} = \mu_s F_n$
• 2.7.B.3 The coefficient of static friction is typically greater than the coefficient of kinetic friction for a given pair of surfaces.

• 2.8.A.1 An ideal spring has negligible mass and exerts a force that is proportional to the change in its length as measured from its relaxed length.
• 2.8.A.2 The magnitude of the force exerted by an ideal spring on an object is given by Hooke's law:
  • Equation: $\vec{F}_s = -k\Delta\vec{x}$
• 2.8.A.3 The force exerted on an object by a spring is always directed toward the equilibrium position of the object–spring system.

• 2.9.A.1 Centripetal acceleration is the component of an object's acceleration directed toward the center of the object's circular path.
  • 2.9.A.1.i The magnitude of centripetal acceleration for an object moving in a circular path is the ratio of the object's tangential speed squared to the radius of the circular path.
    • Equation: $a_c = \dfrac{v^2}{r}$
  • 2.9.A.1.ii Centripetal acceleration is directed toward the center of an object's circular path.
• 2.9.A.2 Centripetal acceleration can result from a single force, more than one force, or components of forces exerted on an object in circular motion.
  • 2.9.A.2.i At the top of a vertical, circular loop, an object requires a minimum speed to maintain circular motion. At this point, and with this minimum speed, the gravitational force is the only force that causes the centripetal acceleration.
    • Equation: $v = \sqrt{gr}$
  • 2.9.A.2.ii Components of the static friction force and the normal force can contribute to the net force producing centripetal acceleration of an object traveling in a circle on a banked surface.
  • 2.9.A.2.iii A component of tension contributes to the net force producing centripetal acceleration experienced by a conical pendulum.
• 2.9.A.3 Tangential acceleration is the rate at which an object's speed changes and is directed tangent to the object's circular path.
• 2.9.A.4 The net acceleration of an object moving in a circle is the vector sum of the centripetal acceleration and tangential acceleration.
• 2.9.A.5 The revolution of an object traveling in a circular path at a constant speed (uniform circular motion) can be described using period and frequency.
  • 2.9.A.5.i The time to complete one full circular path, one full rotation, or a full cycle of oscillatory motion is defined as period, $T$.
  • 2.9.A.5.ii The rate at which an object is completing revolutions is defined as frequency, $f$.
    • Equation: $T = \dfrac{1}{f}$
  • 2.9.A.5.iii For an object traveling at a constant speed in a circular path, the period is given by the derived equation
    • Equation: $T = \dfrac{2\pi r}{v}$

• 2.9.B.1 For a satellite in circular orbit around a central body, the satellite's centripetal acceleration is caused only by gravitational attraction. The period and radius of the circular orbit are related to the mass of the central body.
  • Equation: $T^2 = \dfrac{4\pi^2}{GM} R^3$

Boundary statement: AP Physics 1 only expects students to quantitatively analyze banked curves in which no friction is required to maintain uniform circular motion. Analysis of situations in which friction is required on a banked curve is limited to qualitative descriptions.

Boundary statement: AP Physics 1 does not expect students to know Kepler's first or second laws of planetary motion.