Rectilinear Kinematics (Constant Acceleration)
- v = v0 + a*t
- s = s0 + v0*t + (1/2)*a*t^2
- v^2 = v0^2 + 2*a*(s - s0)
- s = s0 + (1/2)*(v + v0)*t
- For free fall: a = g = 9.81 m/s^2 = 32.2 ft/s^2 (downward positive)
Projectile Motion
- Horizontal: x = v0*cos(theta)*t (constant velocity, no acceleration)
- Vertical: y = v0*sin(theta)*t - (1/2)*g*t^2
- v_x = v0*cos(theta) (constant)
- v_y = v0*sin(theta) - g*t
- Maximum height: h_max = v0^2 * sin^2(theta) / (2g)
- Range: R = v0^2 * sin(2*theta) / g
Newton's Second Law
- F = m*a (net force equals mass times acceleration)
- Sum of F = m * a_G (for translation of center of mass)
- Weight: W = m*g
- Normal and tangential components: F_n = m*a_n, F_t = m*a_t
- Normal acceleration: a_n = v^2/rho (rho = radius of curvature)
Work and Energy
- Work of a force: U = F*d*cos(theta) (constant force)
- Work-energy theorem: T1 + Sum(U) = T2 (kinetic energy plus work)
- Kinetic energy: T = (1/2)*m*v^2
- Gravitational PE: V_g = m*g*h
- Spring PE: V_s = (1/2)*k*x^2
- Conservation of energy: T1 + V1 = T2 + V2 (when only conservative forces act)
- Power: P = dU/dt = F*v
Impulse and Momentum
- Linear momentum: L = m*v
- Impulse: J = F*delta_t = m*v2 - m*v1
- Conservation of momentum: m1*v1 + m2*v2 = m1*v1' + m2*v2' (no external impulse)
- Coefficient of restitution: e = (v2' - v1') / (v1 - v2) for direct central impact
- Perfectly elastic: e = 1; Perfectly plastic: e = 0
Rotational Dynamics
- Angular kinematics: omega = omega0 + alpha*t
- theta = theta0 + omega0*t + (1/2)*alpha*t^2
- omega^2 = omega0^2 + 2*alpha*(theta - theta0)
- Moment equation: Sum(M_G) = I_G * alpha
- Rotational kinetic energy: T = (1/2)*I*omega^2
- Angular momentum: H = I*omega
- Relationship: v = omega*r, a_t = alpha*r, a_n = omega^2*r