PHYS 121 Exam Review: Kinematics, Newton's Laws, Energy, Momentum and Rotation

Terms in this set (32)

1. Displacement vs distanceDisplacement is the vector change in position (final minus initial). Distance is the total path length, a scalar that is never negative.
2. Average velocity vs instantaneous velocityAverage velocity = displacement / elapsed time. Instantaneous velocity is the derivative dx/dt, the slope of the position-time graph at an instant.
3. Constant-acceleration kinematic equationsv = v0 + a*t; x = x0 + v0*t + (1/2)*a*t^2; v^2 = v0^2 + 2*a*(x - x0).
4. Mini-problem: A ball is dropped from rest. How far does it fall in 2.0 s? (g = 9.8 m/s^2)d = (1/2)*g*t^2 = 0.5 * 9.8 * 4.0 = 19.6 m.
5. Projectile motion key ideaHorizontal and vertical motions are independent. Horizontal velocity is constant (no air resistance); vertical acceleration is -g.
6. Range of a projectile launched and landing at the same heightR = v0^2 * sin(2*theta) / g, which is greatest at 45 degrees.
7. Uniform circular motion accelerationCentripetal acceleration a = v^2 / r, directed toward the center, even at constant speed.
8. Newton's first lawAn object stays at rest or moves at constant velocity unless a net external force acts on it (inertia).
9. Newton's second lawF_net = m*a, where F_net is the vector sum of all forces, m is mass in kg and a is acceleration in m/s^2.
10. Newton's third law and a common pitfallForces come in equal and opposite pairs acting on different objects. The normal force and weight on a resting book are not a third-law pair; both act on the book.
11. Mass vs weightMass is the amount of matter (kg), the same everywhere. Weight is the gravitational force on it, W = m*g, measured in newtons.
12. Static vs kinetic frictionStatic friction adjusts up to a maximum f_s <= mu_s*N to prevent sliding. Kinetic friction f_k = mu_k*N acts during sliding. Usually mu_k < mu_s.
13. Block on a frictionless incline at angle theta: acceleration?a = g*sin(theta) down the slope; the normal force is m*g*cos(theta).
14. Atwood machine: two masses m1 > m2 over a frictionless pulley. Acceleration?a = (m1 - m2)*g / (m1 + m2).
15. Work done by a constant forceW = F*d*cos(theta), where theta is the angle between force and displacement. Units: joules (N*m).
16. Work-energy theoremThe net work done on an object equals its change in kinetic energy: W_net = delta KE, with KE = (1/2)*m*v^2.
17. Gravitational and spring potential energyNear Earth, U_g = m*g*h. For a spring, U_s = (1/2)*k*x^2, where k is the spring constant and x the stretch or compression.
18. Conservation of mechanical energyWith only conservative forces doing work, KE + U is constant. Friction converts mechanical energy into thermal energy.
19. Mini-problem: speed at the bottom of a frictionless 5.0 m drop starting from rest?v = sqrt(2*g*h) = sqrt(2 * 9.8 * 5.0), which is about 9.9 m/s.
20. PowerP = W / t = F*v, the rate of doing work, measured in watts (J/s).
21. Momentum and impulseMomentum p = m*v. Impulse J = F_avg * delta_t = delta p.
22. When is total momentum conserved?When the net external force on the system is zero; internal forces in a collision do not change total momentum.
23. Elastic vs perfectly inelastic collisionsBoth conserve momentum. Elastic collisions also conserve kinetic energy. In a perfectly inelastic collision the objects stick together and the most kinetic energy is lost.
24. Mini-problem: 2 kg cart at 3 m/s sticks to a resting 1 kg cart. Final speed?Momentum conservation: 2*3 = (2 + 1)*v, so v = 2 m/s.
25. Center of mass of a system of particlesx_cm = sum(m_i * x_i) / sum(m_i). With no net external force, the center of mass moves at constant velocity.
26. Rotational kinematics links between linear and angular quantitiess = r*theta, v = r*omega, a_tangential = r*alpha, with angles in radians.
27. Torquetau = r*F*sin(theta), the rotational effect of a force about an axis. Newton's second law for rotation: tau_net = I*alpha.
28. Moment of inertia and why it depends on shapeI = sum(m_i * r_i^2): rotational inertia depends on how far mass sits from the axis. A hoop (I = M*R^2) is harder to spin than a solid disk (I = (1/2)*M*R^2).
29. Rotational kinetic energy and rolling without slippingKE_rot = (1/2)*I*omega^2. For rolling without slipping v = R*omega and total KE = (1/2)*m*v^2 + (1/2)*I*omega^2.
30. Conservation of angular momentumL = I*omega is constant when net external torque is zero. A skater pulling in her arms lowers I, so omega increases.
31. Conditions for static equilibriumNet force is zero and net torque about any axis is zero.
32. Hooke's law and simple harmonic motion periodF = -k*x. A mass on a spring oscillates with period T = 2*pi*sqrt(m/k), independent of amplitude.