Vectors & Kinematics
A vector has what two characteristics?
Magnitude and Direction
State Newton’s First Law.
Objects in motion stay in motion unless acted on by a net force.
Write the Work–Energy Theorem.
W_net = ΔK.
Write the relation for rolling without slipping.
v = Rω.
Pressure in a fluid increases with what variable?
Depth.
Write the x- and y- components of a vector with a magnitude of 12 at 30 degrees.
(12 cos30, 12 sin30)
The normal force on a flat horizontal surface equals what?
mg
Kinetic energy for a mass m moving at speed v is what?
(1/2) m v².
Define torque.
τ = r × F.
State Pascal’s law.
Pressure applied to a confined fluid is transmitted equally throughout.
If velocity is constant what is the acceleration?
0
Static friction adjusts up to what maximum value?
μ_s N.
Momentum is always conserved in what type of system?
Isolated system (no external forces).
The moment of inertia depends on what two physical quantities?
Mass and how it is distributed relative to the axis.
Bernoulli’s equation applies to what type of flow?
Incompressible, non-viscous flow.
A ball is thrown straight up. At the very top, what is the velocity and what is the acceleration?
v = 0, a = –g.
A car turns in a circle at constant speed. Is the acceleration zero? Why or why not?
No — direction changes, so acceleration exists toward the center.
In an inelastic collision, which quantity is NOT conserved: momentum or kinetic energy?
kinetic energy
Angular momentum is conserved when what is zero?
Net external torque.
A mass–spring oscillator has period T = 2π√(m/k). If mass increases, what happens to T?
T increases.
A projectile launched at speed v0 at angle θ has what horizontal acceleration?
0
Write Newton’s Second Law.
F_net = m a.
A 2-kg cart moving at 3 m/s collides and sticks to a 4-kg cart at rest. What is the final velocity?
(2*3 + 4*0)/6 = 1 m/s.
A disk with I = 0.20 kg·m² has a net torque of 4.0 N·m. What is its angular acceleration?
α = τ/I = 20 rad/s².
A mass oscillates with amplitude A and angular frequency ω. What is the maximum speed?
v_max = Aω.