1.2 The Fundamental Equation of Dynamics

Irodov Problems 1.59 to 1.117.

59problems
123figures
Difficulty3.1avgDifficulty: 0 rated 1, 10 rated 2, 32 rated 3, 16 rated 4, 1 rated 5; mean 3.1.
Uniqueness3.4avgUniqueness: 0 rated 1, 5 rated 2, 29 rated 3, 20 rated 4, 5 rated 5; mean 3.4.

No.	Title	Difficulty	Uniqueness	Methods
1.59	Ballast Traded for Reversed Acceleration	Difficulty 2 of 5	Uniqueness 3 of 5	newton second law · free body · limiting cases
1.60	Which Thread Ties the Two Riders	Difficulty 3 of 5	Uniqueness 3 of 5	newton second law · friction · constraints pulleys · free body
1.61	The Trailing Bar Pushes Back	Difficulty 3 of 5	Uniqueness 4 of 5	newton second law · friction · free body · limiting cases
1.62	Why Going Up Takes Less Time	Difficulty 2 of 5	Uniqueness 2 of 5	newton second law · free body · friction · limiting cases
1.63	Three Ways the Ratio Can Go	Difficulty 3 of 5	Uniqueness 3 of 5	newton second law · friction · constraints pulleys
1.64	Which Way Once It Finally Moves	Difficulty 2 of 5	Uniqueness 2 of 5	newton second law · friction · constraints pulleys
1.65	Friction's Ceiling Freezes the Plank	Difficulty 3 of 5	Uniqueness 3 of 5	newton second law · friction · free body · kinematic graphs
1.66	Fixed Base, Free Angle	Difficulty 3 of 5	Uniqueness 3 of 5	optimization · newton second law · friction · calculus of motion
1.67	Angling the Pull to Save Tension	Difficulty 3 of 5	Uniqueness 4 of 5	newton second law · friction · optimization
1.68	When the Normal Force Vanishes	Difficulty 3 of 5	Uniqueness 4 of 5	newton second law · free body · calculus of motion · limiting cases
1.69	Work Only Sees the Angle	Difficulty 3 of 5	Uniqueness 4 of 5	work energy · calculus of motion · limiting cases
1.70	The Reeling Motor Chases Itself	Difficulty 3 of 5	Uniqueness 3 of 5	newton second law · friction · free body · momentum conservation
1.71	An Elevator Makes Gravity Stronger	Difficulty 3 of 5	Uniqueness 3 of 5	newton second law · non inertial frame · constraints pulleys · free body
1.72	One Movable Pulley, Two Tensions	Difficulty 4 of 5	Uniqueness 4 of 5	constraints pulleys · newton second law · free body
1.73	The Pulley That Rides Its Own Rope	Difficulty 4 of 5	Uniqueness 4 of 5	newton second law · constraints pulleys · free body · limiting cases
1.74	The Free Strand Pins the Friction	Difficulty 4 of 5	Uniqueness 5 of 5	newton second law · constraints pulleys · friction · free body
1.75	A Second Pulley Halves the Pull	Difficulty 4 of 5	Uniqueness 3 of 5	newton second law · constraints pulleys · free body
1.76	The String That Goes Slack Mid Flight	Difficulty 3 of 5	Uniqueness 4 of 5	newton second law · constraints pulleys · free body · calculus of motion
1.77	One Contact Point Links Two Accelerations	Difficulty 3 of 5	Uniqueness 4 of 5	newton second law · free body · vector decomposition
1.78	A Peg Anchored Thread Drags the Block	Difficulty 4 of 5	Uniqueness 5 of 5	newton second law · constraints pulleys · friction · free body
1.79	Excess Tension Turns into Backward Friction	Difficulty 3 of 5	Uniqueness 4 of 5	newton second law · friction · constraints pulleys · free body
1.80	Too Much Push Slides the Bar Uphill	Difficulty 3 of 5	Uniqueness 3 of 5	newton second law · non inertial frame · friction · vector decomposition
1.81	Gravity Slides Both Bodies at Once	Difficulty 3 of 5	Uniqueness 3 of 5	newton second law · vector decomposition · free body
1.82	A Fixed Anchor Moves the Wedge	Difficulty 4 of 5	Uniqueness 4 of 5	newton second law · constraints pulleys · free body · vector decomposition
1.83	A Quarter Turn Rotates Away Its Own Average	Difficulty 3 of 5	Uniqueness 4 of 5	impulse · circular motion · vector decomposition · calculus of motion
1.84	The Middle of the Loop Needs Two Axes	Difficulty 3 of 5	Uniqueness 3 of 5	newton second law · circular motion · vector decomposition
1.85	Two Parts Share One Critical Angle	Difficulty 4 of 5	Uniqueness 5 of 5	newton second law · circular motion · energy conservation · calculus of motion
1.86	Where Tangential Meets Centripetal in Magnitude	Difficulty 3 of 5	Uniqueness 3 of 5	newton second law · circular motion · energy conservation
1.87	Gravity Outruns the Normal Force	Difficulty 3 of 5	Uniqueness 3 of 5	newton second law · circular motion · energy conservation
1.88	Spring Against Centrifugal Pull	Difficulty 3 of 5	Uniqueness 3 of 5	non inertial frame · newton second law · circular motion
1.89	Fading Friction Picks an Optimal Radius	Difficulty 2 of 5	Uniqueness 3 of 5	newton second law · circular motion · optimization
1.90	The Growing Centripetal Share	Difficulty 2 of 5	Uniqueness 2 of 5	newton second law · circular motion · friction
1.91	The Crest Is Really the Worst Case	Difficulty 3 of 5	Uniqueness 3 of 5	newton second law · friction · circular motion · optimization
1.92	Hoop Stress Splits into Two Causes	Difficulty 4 of 5	Uniqueness 4 of 5	newton second law · circular motion · free body
1.93	Why the Two Tensions Differ	Difficulty 4 of 5	Uniqueness 4 of 5	newton second law · friction · differential equation · constraints pulleys
1.94	Gravity Never Touches the Push	Difficulty 3 of 5	Uniqueness 4 of 5	newton second law · circular motion · vector decomposition
1.95	An Ellipse Centered, Not Focused	Difficulty 2 of 5	Uniqueness 3 of 5	newton second law · vector decomposition · differential equation
1.96	Momentum Keeps No Memory of Launch	Difficulty 2 of 5	Uniqueness 3 of 5	newton second law · impulse · projectile
1.97	The Force That Rises Then Fades	Difficulty 2 of 5	Uniqueness 2 of 5	newton second law · impulse · differential equation
1.98	Distance Under a Sinusoidal Push	Difficulty 2 of 5	Uniqueness 3 of 5	newton second law · differential equation · limiting cases
1.99	A Push That Turns Off and Coasts	Difficulty 2 of 5	Uniqueness 3 of 5	newton second law · differential equation · symmetry
1.100	The Boat That Never Stops	Difficulty 3 of 5	Uniqueness 3 of 5	newton second law · differential equation · limiting cases · kinematic graphs
1.101	Trading Depth for Time in a Plank	Difficulty 3 of 5	Uniqueness 3 of 5	newton second law · differential equation · limiting cases
1.102	The Friction That Catches Up	Difficulty 3 of 5	Uniqueness 3 of 5	newton second law · friction · differential equation · calculus of motion
1.103	Waiting Out the Friction Threshold	Difficulty 3 of 5	Uniqueness 3 of 5	newton second law · friction · differential equation
1.104	Drag Costs More Going Up	Difficulty 4 of 5	Uniqueness 4 of 5	newton second law · differential equation · limiting cases
1.105	The Hodograph Is a Circle	Difficulty 3 of 5	Uniqueness 4 of 5	newton second law · calculus of motion · vector decomposition
1.106	The Friction Coefficient That Cancels Gravity	Difficulty 4 of 5	Uniqueness 4 of 5	newton second law · friction · differential equation
1.107	One Coordinate Carries the Whole Chain	Difficulty 4 of 5	Uniqueness 3 of 5	energy conservation · potential energy · differential equation
1.108	The Push That Frees the Body Early	Difficulty 4 of 5	Uniqueness 4 of 5	non inertial frame · newton second law · energy conservation
1.109	When A Circular Orbit Resists Nudging	Difficulty 4 of 5	Uniqueness 5 of 5	stability analysis · differential equation · circular motion
1.110	Two Equilibria on a Spinning Hoop	Difficulty 4 of 5	Uniqueness 4 of 5	non inertial frame · stability analysis · circular motion · newton second law
1.111	The Rifle That Cannot Aim True North	Difficulty 3 of 5	Uniqueness 3 of 5	non inertial frame · vector decomposition · frames of reference
1.112	A Radial Slide Wakes Fictitious Forces	Difficulty 3 of 5	Uniqueness 3 of 5	non inertial frame · newton second law · vector decomposition
1.113	The Sleeve Speeds Before It Deflects	Difficulty 3 of 5	Uniqueness 3 of 5	non inertial frame · differential equation · newton second law
1.114	Where the Two Fictitious Forces Cancel	Difficulty 5 of 5	Uniqueness 5 of 5	non inertial frame · vector decomposition · circular motion
1.115	Friction-Free Slide, Rotating Only Underneath	Difficulty 4 of 5	Uniqueness 4 of 5	non inertial frame · energy conservation · circular motion · vector decomposition
1.116	The Earth Presses Every Train Sideways	Difficulty 3 of 5	Uniqueness 3 of 5	non inertial frame · vector decomposition · frames of reference
1.117	Every Falling Object Lands East	Difficulty 3 of 5	Uniqueness 2 of 5	non inertial frame · differential equation · approximation expansion