🎡AP Physics 1 Unit 2 – Dynamics

Key Concepts and Definitions

• Dynamics studies the forces that cause objects to move and how those forces affect the motion of objects
• Force is a push or pull on an object that can cause it to accelerate, decelerate, or change direction
• Mass is a measure of the amount of matter in an object and determines its resistance to acceleration
• Acceleration is the rate of change of velocity over time and is caused by net forces acting on an object
• Friction is a force that opposes motion between two surfaces in contact and can be static or kinetic
  • Static friction prevents an object from moving when a force is applied
  • Kinetic friction slows down an object that is already in motion
• Inertia is the tendency of an object to resist changes in its motion and is directly proportional to its mass
• Center of mass is the point where the entire mass of an object can be considered to be concentrated

Newton's Laws of Motion

• Newton's First Law of Motion states that an object at rest stays at rest, and an object in motion stays in motion with constant velocity, unless acted upon by a net external force
• Newton's Second Law of Motion states that the acceleration of an object is directly proportional to the net force acting on it and inversely proportional to its mass, expressed as $F = ma$
• Newton's Third Law of Motion states that for every action, there is an equal and opposite reaction
  • If object A exerts a force on object B, then object B exerts an equal and opposite force on object A
• The net force on an object is the vector sum of all the forces acting on it
• An object in equilibrium has a net force of zero and no acceleration
• Objects with constant acceleration have a net force that is constant in both magnitude and direction
• Objects with varying acceleration have a net force that changes in magnitude, direction, or both over time

Forces and Free-Body Diagrams

• A free-body diagram is a visual representation of all the forces acting on an object, drawn as vectors with their magnitudes and directions
• The normal force is the force exerted by a surface on an object that is perpendicular to the surface
• The gravitational force is the force of attraction between two objects with mass and is directed toward the center of the Earth
  • The magnitude of the gravitational force on an object near Earth's surface is given by $F_g = mg$, where $g$ is the acceleration due to gravity ($9.8 m/s^2$)
• Tension is the force exerted by a rope, string, or cable on an object when it is pulled taut
• The force of friction always acts parallel to the surface and opposite to the direction of motion or potential motion
• Air resistance is a type of fluid friction that opposes the motion of objects moving through the air
• Applied forces are forces that are exerted on an object by another object or by an external agent (pushing a box)

Kinematics Equations

• Kinematics equations describe the motion of an object without considering the forces that cause the motion
• The equations relate displacement ($\Delta x$), initial velocity ($v_0$), final velocity ($v$), acceleration ($a$), and time ($t$)
  • $v = v_0 + at$
  • $\Delta x = v_0t + \frac{1}{2}at^2$
  • $v^2 = v_0^2 + 2a\Delta x$
  • $\Delta x = \frac{1}{2}(v_0 + v)t$
• These equations are valid only for objects with constant acceleration
• To solve problems using kinematics equations, identify the known and unknown variables, choose the appropriate equation, and solve for the unknown variable
• Kinematics equations can be used to analyze the motion of objects in one dimension (along a straight line) or in two dimensions (projectile motion)

Work, Energy, and Power

• Work is the product of the force exerted on an object and the distance the object moves in the direction of the force, expressed as $W = Fd\cos\theta$
  • $\theta$ is the angle between the force and the displacement vectors
  • Work is a scalar quantity measured in joules (J)
• Energy is the capacity to do work and can be in the form of kinetic, potential, or other types of energy
• Kinetic energy is the energy an object possesses due to its motion, given by $KE = \frac{1}{2}mv^2$
• Potential energy is the energy an object possesses due to its position or configuration
  • Gravitational potential energy is given by $PE = mgh$, where $h$ is the height of the object above a reference level
• The work-energy theorem states that the net work done on an object is equal to the change in its kinetic energy
• Power is the rate at which work is done or energy is transferred, expressed as $P = \frac{W}{t}$ and measured in watts (W)

Momentum and Collisions

• Momentum is the product of an object's mass and velocity, expressed as $p = mv$
  • Momentum is a vector quantity measured in kg·m/s
• The law of conservation of momentum states that the total momentum of a closed system remains constant
  • In a closed system, the total momentum before an interaction (collision) equals the total momentum after the interaction
• Elastic collisions are collisions in which both momentum and kinetic energy are conserved (bouncing balls)
• Inelastic collisions are collisions in which momentum is conserved, but kinetic energy is not (colliding cars)
• Perfectly inelastic collisions are collisions in which the colliding objects stick together after the collision
• The impulse-momentum theorem states that the impulse (force multiplied by time) applied to an object equals the change in its momentum
  • $J = F\Delta t = \Delta p = m\Delta v$

Rotational Motion

• Angular displacement is the angle through which an object rotates about an axis and is measured in radians (rad)
• Angular velocity is the rate of change of angular displacement over time, expressed as $\omega = \frac{\Delta\theta}{\Delta t}$ and measured in rad/s
• Angular acceleration is the rate of change of angular velocity over time, expressed as $\alpha = \frac{\Delta\omega}{\Delta t}$ and measured in rad/s²
• Torque is the rotational equivalent of force and causes an object to rotate about an axis, given by $\tau = rF\sin\theta$
  • $r$ is the distance from the axis of rotation to the point where the force is applied
  • $\theta$ is the angle between the force and the radius vectors
• Moment of inertia is the rotational equivalent of mass and determines an object's resistance to angular acceleration, given by $I = \sum mr^2$
• The rotational kinematics equations are analogous to the linear kinematics equations, with angular variables replacing linear variables
  • $\omega = \omega_0 + \alpha t$
  • $\Delta\theta = \omega_0t + \frac{1}{2}\alpha t^2$
  • $\omega^2 = \omega_0^2 + 2\alpha\Delta\theta$

Problem-Solving Strategies

• Read the problem carefully and identify the given information and the quantity to be determined
• Draw a diagram of the situation, including a free-body diagram if forces are involved
• List the known and unknown variables, and assign symbols to each
• Determine which concepts, principles, or equations are relevant to the problem
• Solve the problem symbolically first, and then substitute the known values to obtain a numerical answer
• Check the units of the answer to ensure they are consistent with the quantity being determined
• Evaluate the reasonableness of the answer based on the problem's context and your understanding of the concepts involved
• If the problem involves multiple steps, work through each step systematically and check your work at each stage