Lesson 11 of 11 · 16 min
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Must-know facts
17 facts
- 01Mass is the measure of inertia; heavier bodies are harder to start, stop or turn.
- 02F = dp/dt; for constant mass F = ma. 1 N = 1 kg m s⁻².
- 03Impulse = FΔt = Δp; unit N s, same as momentum.
- 04Rebound: Δp = m(v₁ + v₂) in magnitude because the velocity reverses.
- 05Action and reaction never cancel each other: the two act on different bodies.
- 06Weight of a book and the normal force on it are balancing forces on one body, not a third-law pair.
- 07Total momentum of an isolated system is conserved; recoil speed of a gun is (m_bullet/m_gun) × bullet speed.
- 08Static friction is self-adjusting: f_s ≤ μ_s N; it equals μ_s N only at the point of slipping.
- 09Kinetic friction f_k = μ_k N, and usually μ_k < μ_s.
- 10Limiting friction does not depend on the area of contact.
- 11Rolling friction is far smaller than sliding friction.
- 12Apparent weight in a lift = m(g + a) for upward acceleration and m(g − a) for downward acceleration; zero in free fall.
- 13Maximum speed on a level curve: v = √(μ_s R g), independent of mass.
- 14Optimum speed on a banked curve (no friction needed): v₀ = √(R g tan θ).
- 15Atwood machine: a = (m₁ − m₂)g/(m₁ + m₂), T = 2m₁m₂g/(m₁ + m₂).
- 16Tension is the same throughout a light string over a frictionless pulley.
- 17Acceleration at an instant depends only on the net force at that instant.
Common traps
Where marks are lost
Formulas
16 to know
Linear momentum
p = mv
Vector along v; SI unit kg m s⁻¹.
Newton's second law
F = dp/dt = ma
F is the net external force; F = ma for constant mass.
Impulse
J = FΔt = Δp = m(v − u)
F is the average force during the short time Δt; unit N s.
Newton's third law
F_AB = −F_BA
The two forces act on different bodies.
Conservation of momentum (two bodies)
m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂
Isolated system; velocities relative to the ground, with signs.
Recoil velocity
V = −(m/M)v
M, V for the gun; m, v for the bullet; starting from rest.
Equilibrium of a particle
ΣFx = 0, ΣFy = 0
Resolve forces along perpendicular axes.
Static friction
f_s ≤ μ_s N, (f_s)max = μ_s N
Self-adjusting up to the limiting value.
Kinetic friction
f_k = μ_k N
Usually μ_k < μ_s.
Spring force
F = −kx
Restoring force for small deformation x; k in N m⁻¹.
Apparent weight in a lift
R = m(g + a) upward acceleration; R = m(g − a) downward acceleration
R is the normal force (scale reading).
Centripetal force
F = mv²/R
Directed towards the centre of the circle.
Maximum speed on a level road
v_max = √(μ_s R g)
Independent of mass.
Maximum speed on a banked road
v_max = √[R g (μ_s + tan θ)/(1 − μ_s tan θ)]
θ is the banking angle.
Optimum speed on a banked road
v₀ = √(R g tan θ)
Friction not needed at this speed.
Two masses over a pulley (Atwood)
a = (m₁ − m₂)g/(m₁ + m₂), T = 2m₁m₂g/(m₁ + m₂)
Light inextensible string, frictionless light pulley, m₁ > m₂.
Key terms
14 terms
- Inertia
- The tendency of a body to keep its state of rest or uniform straight-line motion.
- Inertial frame
- A reference frame in which a body with no net force on it moves with constant velocity.
- Linear momentum
- Mass times velocity; the quantity whose rate of change equals the net force.
- Impulse
- The product of a large force and the short time it acts, equal to the change of momentum it produces.
- Newton
- The force that gives a 1 kg mass an acceleration of 1 m s⁻².
- Normal reaction
- The part of a contact force perpendicular to the surfaces in contact.
- Tension
- The pulling force a stretched string or rope exerts on whatever is attached to it.
- Static friction
- Friction that prevents sliding from starting; adjusts in size up to a limit.
- Limiting friction
- The largest static friction, μ_s N, reached just before sliding begins.
- Kinetic friction
- Friction that acts while surfaces slide over each other, μ_k N.
- Rolling friction
- The small resistance to a body rolling over a surface.
- Centripetal force
- The net inward force needed to keep a body moving in a circle.
- Banking of roads
- Raising the outer edge of a curved road so that the normal force helps provide the centripetal force.
- Free-body diagram
- A sketch of one body showing all the external forces acting on it.