Forces and circular motion formulas

Fnet = all forces along the motion, with signs (type 310+420−610 or 26cos(22)). At rest or steady speed: a = 0. Scale, rope or floor holding m: type 9.8+a in the a box (a − if down). Tied blocks: Fnet = weights pulling, with signs (Atwood 5*9.8−3*9.8), m = total (5+3). Then use Fnet = ma on one block with every force on it, e.g. Atwood T − m₁g = m₁a so T = m₁(g + a). 3rd law: same force on both.

Level floor, nothing else pushing up or down: normal force N = mg. Hanging at rest: rope tension = mg (one rope holding two: m box 92+58). Pulley, 2 rope pieces hold the load: each pulls half (m box 42/2). Ramp: N = mgcosθ, type 7cos(38) in the m box. Pushed down with F: N = mg + F. Pulled up: N = mg − F. Moon: g = 1.62. Mass is the same everywhere.

μₛ (static): most it can hold = push that just starts it moving. μₖ (kinetic): while it slides. Not moving, not about to slip: friction = the push. N on level floor = mg: type 25*9.8 in the N box. On a ramp: type 7*9.8cos(38) in the N box. Rope pulling up at θ: N = mg − Fsinθ, type 20*9.8−90sin(25).

a = acceleration DOWN the ramp. μ = μₖ while it slides. Frictionless: μ = 0. Level floor: θ = 0, so a = −μg (slowing down). Angle where it just starts to slide: a = 0, μ = μₛ. Sliding UP the ramp: type μ as −μₖ (a is still + down the ramp). Ramp normal force: W = mg with 7cos(38) in the m box.

a points to the center. Divide by 9.8 for g's. Force toward the center (string, tube): Fnet = ma with this a (a box: 16²/15). Speed from lap time T: type 2π*r/T in the v box; PLUG IN shows v (3 rev/s: T = 1/3; rpm: T = 60/rpm). Know v and T: type v*T/(2π) in the r box. Flat curve, top speed before skidding: a = μₛ*9.8. Banked curve, no friction: a = 9.8tan(θ). Top of a hill, car leaving the road: a = 9.8.

Terminal speed: air drag = weight, so it stops speeding up. ρ = 1.2 for air (change it if the problem gives one). C = drag coefficient (no unit). A = area facing the air (m²). 4 times the mass: 2 times the speed.