Physics Kinematics and Dynamics Concepts

Kinematic Equations

• Fourth kinematic equation: ∆x = 1/2(Vf + Vo)t, relating displacement, initial and final velocity, and time.

Forces and Energy

• The relationship between conservative forces and potential energy is given by: F = -dU/dx, where F is the force and U is potential energy.

Collision Equations

• Essential collision equation: V1 - V2 = -(V1' - V2'), represents the relationship between initial and final velocities in one-dimensional elastic collisions.
• Helpful collision equations:
  • V1' = (m1 - m2)/(m1 + m2)V1, calculates the final velocity of object 1 after collision.
  • V2 = 2m1/(m1+m2)V1, calculates the final velocity of object 2 after collision.

Rotational Motion

• Non-slip conditions are stated as Vcm = rw (where Vcm is the center of mass velocity, r is radius, and w is angular velocity) and acm = ra (with a being linear acceleration and alpha as angular acceleration).

Moment of Inertia

• Parallel axis theorem formula: I = Icm + md², where I is the moment of inertia about an arbitrary axis, Icm is the moment of inertia about a parallel axis through the center of mass, m is mass, and d is the distance between the axes.

Momentum Conservation

• Conditions for conservation of momentum: Fext = 0 implies that net external force is zero, resulting in dp/dt = 0, meaning momentum is conserved.

Simple Harmonic Motion (SHM)

• Condition for simple harmonic motion is given by d²x/dt² = a = -w²x, where x is displacement and w is angular frequency.
• Velocity for simple harmonic motion formulated as V = -Awsin(wt) with Vmax defined as Vmax = Aw, where A is amplitude and wt is angular position over time.
• Acceleration for simple harmonic motion expressed as a = -Aw²cos(wt), with maximum acceleration amax = Aw².

Circular Motion

• Arc length is defined as s = rø, where s is arc length, r is radius, and θ is angle in radians.