1.3 Laws of Conservation

Irodov Problems 1.118 to 1.199.

82problems
114figures
Difficulty3.0avgDifficulty: 2 rated 1, 19 rated 2, 44 rated 3, 14 rated 4, 3 rated 5; mean 3.0.
Uniqueness3.3avgUniqueness: 1 rated 1, 10 rated 2, 40 rated 3, 26 rated 4, 5 rated 5; mean 3.3.

No.	Title	Difficulty	Uniqueness	Methods
1.118	Only the Endpoints Ever Mattered	Difficulty 1 of 5	Uniqueness 2 of 5	work energy · vector decomposition
1.119	Square-Root Speed Hides Constant Acceleration	Difficulty 2 of 5	Uniqueness 2 of 5	work energy · calculus of motion · differential equation
1.120	Differentiating Energy Yields Only Tangential Force	Difficulty 2 of 5	Uniqueness 3 of 5	work energy · circular motion · vector decomposition
1.121	Only Height and Base Length Matter	Difficulty 3 of 5	Uniqueness 4 of 5	work energy · friction · potential energy
1.122	Matching Speeds Link Slope and Floor	Difficulty 3 of 5	Uniqueness 3 of 5	work energy · friction · energy conservation
1.123	The Turning Point Sets the Minimum	Difficulty 4 of 5	Uniqueness 4 of 5	work energy · friction · optimization
1.124	Integrating Friction as the Chain Leaves	Difficulty 3 of 5	Uniqueness 3 of 5	work energy · friction · energy conservation
1.125	Power Oscillates Yet Averages to Zero	Difficulty 2 of 5	Uniqueness 3 of 5	work energy · projectile · limiting cases
1.126	Constant Push Behind a Quadratic Pull	Difficulty 2 of 5	Uniqueness 3 of 5	work energy · circular motion · calculus of motion
1.127	Friction Sets Its Own Speed Limit	Difficulty 3 of 5	Uniqueness 3 of 5	work energy · friction · optimization · differential equation
1.128	Centrifugal Work Only Reads the Radius	Difficulty 2 of 5	Uniqueness 2 of 5	non inertial frame · potential energy · work energy
1.129	Series Springs Split the Stretch	Difficulty 2 of 5	Uniqueness 3 of 5	work energy · potential energy · optimization
1.130	Half the Climb, Three Quarters the Work	Difficulty 3 of 5	Uniqueness 3 of 5	newton second law · work energy · potential energy
1.131	Not at Equilibrium, the Force Peaks	Difficulty 3 of 5	Uniqueness 3 of 5	potential energy · stability analysis · optimization · dimensional analysis
1.132	Unequal Stiffness Makes the Field Elliptical	Difficulty 3 of 5	Uniqueness 4 of 5	potential energy · vector decomposition · symmetry
1.133	One Field Curls, One Does Not	Difficulty 2 of 5	Uniqueness 2 of 5	potential energy · vector decomposition
1.134	Friction Doubles Up Against Gravity Uphill	Difficulty 2 of 5	Uniqueness 2 of 5	newton second law · friction · work energy
1.135	Optimal Shelf Height Maximizes Landing Range	Difficulty 3 of 5	Uniqueness 3 of 5	energy conservation · projectile · optimization
1.136	Loop Break-Off Height Fixes Apex Speed	Difficulty 4 of 5	Uniqueness 4 of 5	energy conservation · newton second law · circular motion · projectile
1.137	Shifted Pivot Becomes a Vertical Circle	Difficulty 3 of 5	Uniqueness 4 of 5	frames of reference · energy conservation · newton second law · circular motion
1.138	Winding Thread Spirals Disc Inward	Difficulty 5 of 5	Uniqueness 5 of 5	vector decomposition · differential equation · work energy
1.139	Falling Sleeve Stretches the Rubber Cord	Difficulty 3 of 5	Uniqueness 3 of 5	energy conservation · elastic energy
1.140	When the Spring Pulls It Off	Difficulty 4 of 5	Uniqueness 4 of 5	energy conservation · newton second law · free body · constraints pulleys
1.141	Elastic Cord Angle Signals Slipping Onset	Difficulty 4 of 5	Uniqueness 4 of 5	work energy · elastic energy · friction · newton second law
1.142	The Cost of Spinning Up Slowly	Difficulty 3 of 5	Uniqueness 3 of 5	newton second law · energy conservation · elastic energy · circular motion
1.143	Why the Center Never Rises	Difficulty 2 of 5	Uniqueness 3 of 5	newton second law · constraints pulleys · center of mass
1.144	Reflect the Trajectory Through the Center	Difficulty 2 of 5	Uniqueness 4 of 5	momentum conservation · center of mass · symmetry
1.145	A Ring Obeys the Conical Pendulum	Difficulty 2 of 5	Uniqueness 3 of 5	newton second law · center of mass · circular motion · free body
1.146	Friction Steers a Precessing Rolling Cone	Difficulty 4 of 5	Uniqueness 3 of 5	newton second law · friction · rolling · center of mass
1.147	The CM Frame Minimizes Kinetic Energy	Difficulty 2 of 5	Uniqueness 3 of 5	momentum conservation · center of mass · optimization · frames of reference
1.148	Energy Splits into Internal and Bulk	Difficulty 2 of 5	Uniqueness 3 of 5	frames of reference · center of mass · momentum conservation
1.149	Relative Velocity Alone Carries Internal Energy	Difficulty 3 of 5	Uniqueness 3 of 5	center of mass · momentum conservation · energy conservation · vector decomposition
1.150	Gravity Moves the Center Like One Particle	Difficulty 2 of 5	Uniqueness 2 of 5	momentum conservation · center of mass · newton second law · calculus of motion
1.151	Wall Reaction Decides When It Lets Go	Difficulty 3 of 5	Uniqueness 4 of 5	energy conservation · momentum conservation · center of mass
1.152	A Sudden Force Doubles the Stretch	Difficulty 4 of 5	Uniqueness 4 of 5	newton second law · relative motion · energy conservation · differential equation
1.153	The Threshold Where the Floor Lets Go	Difficulty 5 of 5	Uniqueness 5 of 5	energy conservation · newton second law · center of mass
1.154	A Perpendicular Jump Keeps Its Speed	Difficulty 3 of 5	Uniqueness 4 of 5	momentum conservation · collisions · vector decomposition
1.155	A Relative Jump, Measured at Landing	Difficulty 3 of 5	Uniqueness 3 of 5	momentum conservation · collisions · frames of reference
1.156	Sequential Recoil Beats Simultaneous Jump	Difficulty 3 of 5	Uniqueness 3 of 5	momentum conservation · limiting cases
1.157	Falling Links Double the Push	Difficulty 3 of 5	Uniqueness 4 of 5	momentum flux · impulse · dimensional analysis
1.158	Infinitely Many Bounces, Finite Momentum	Difficulty 3 of 5	Uniqueness 3 of 5	impulse · collisions · energy conservation
1.159	Raft Recoils While Man Walks	Difficulty 3 of 5	Uniqueness 3 of 5	center of mass · momentum conservation · newton second law
1.160	Climbing Man Shifts the Whole System	Difficulty 4 of 5	Uniqueness 4 of 5	center of mass · constraints pulleys · newton second law
1.161	The Shot That Stops a Sliding Cannon	Difficulty 3 of 5	Uniqueness 3 of 5	momentum conservation · impulse · newton second law
1.162	Bifilar Pendulum as a Ballistic Scale	Difficulty 3 of 5	Uniqueness 3 of 5	momentum conservation · energy conservation · collisions
1.163	Breaking Off at a Shared Speed	Difficulty 3 of 5	Uniqueness 3 of 5	momentum conservation · energy conservation
1.164	Heat That Doesn't Care Who's Watching	Difficulty 3 of 5	Uniqueness 3 of 5	energy conservation · momentum conservation · work energy · frames of reference
1.165	The Falling Frame Meets Relative Rest	Difficulty 3 of 5	Uniqueness 4 of 5	frames of reference · relative motion · calculus of motion
1.166	Merge Two Momenta, Component by Component	Difficulty 1 of 5	Uniqueness 1 of 5	momentum conservation · collisions · vector decomposition
1.167	Reduced Mass Absorbs the Lost Energy	Difficulty 3 of 5	Uniqueness 3 of 5	momentum conservation · collisions · center of mass
1.168	Perpendicular Recoil, Full Stop Head-On	Difficulty 3 of 5	Uniqueness 2 of 5	momentum conservation · energy conservation · collisions · vector decomposition
1.169	Elastic Collision Reveals the Mass Ratio	Difficulty 3 of 5	Uniqueness 3 of 5	momentum conservation · energy conservation · collisions
1.170	Only the Normal Component Compresses	Difficulty 3 of 5	Uniqueness 4 of 5	momentum conservation · energy conservation · collisions · vector decomposition
1.171	Sharing the Bonus Energy Unevenly	Difficulty 4 of 5	Uniqueness 4 of 5	momentum conservation · energy conservation · optimization · collisions
1.172	The Ordering Rule Picks the Root	Difficulty 3 of 5	Uniqueness 3 of 5	momentum conservation · energy conservation · collisions
1.173	The Forty Percent That Vanished	Difficulty 3 of 5	Uniqueness 3 of 5	momentum conservation · energy conservation · collisions · vector decomposition
1.174	Perpendicular Speeds Are a Right Triangle	Difficulty 2 of 5	Uniqueness 2 of 5	momentum conservation · center of mass · energy conservation
1.175	Tangent to the Momentum Circle	Difficulty 4 of 5	Uniqueness 4 of 5	collisions · momentum conservation · center of mass · vector decomposition
1.176	Two Simultaneous Contacts, One Symmetry	Difficulty 4 of 5	Uniqueness 5 of 5	collisions · momentum conservation · energy conservation · vector decomposition
1.177	The Right Angle Hidden in Momentum	Difficulty 2 of 5	Uniqueness 3 of 5	momentum conservation · energy conservation · collisions · vector decomposition
1.178	The System Must Include the Exhaust	Difficulty 3 of 5	Uniqueness 3 of 5	variable mass · impulse · momentum flux · frames of reference
1.179	Speed Is the Log of Mass	Difficulty 3 of 5	Uniqueness 4 of 5	variable mass · momentum conservation · differential equation · relative motion
1.180	Constant Acceleration Sets an Exponential Mass	Difficulty 2 of 5	Uniqueness 2 of 5	variable mass · differential equation · newton second law
1.181	Sideways Thrust Rotates Without Slowing	Difficulty 3 of 5	Uniqueness 4 of 5	variable mass · differential equation · momentum conservation
1.182	Leaking Sand Never Pushes Back	Difficulty 3 of 5	Uniqueness 3 of 5	variable mass · newton second law · momentum conservation · differential equation
1.183	Sand That Joins Steals Momentum	Difficulty 3 of 5	Uniqueness 4 of 5	variable mass · newton second law · momentum conservation · differential equation
1.184	The Hanging Length Stays Fixed	Difficulty 5 of 5	Uniqueness 5 of 5	variable mass · newton second law · differential equation · limiting cases
1.185	Torque Stays Fixed While Momentum Turns	Difficulty 3 of 5	Uniqueness 3 of 5	angular momentum · vector decomposition · calculus of motion
1.186	Angular Momentum Grows as Time Squared	Difficulty 3 of 5	Uniqueness 3 of 5	angular momentum · projectile · calculus of motion
1.187	Only the Perpendicular Line Escapes Torque	Difficulty 3 of 5	Uniqueness 4 of 5	angular momentum · impulse · vector decomposition
1.188	Which Point Keeps the Momentum Fixed	Difficulty 4 of 5	Uniqueness 4 of 5	angular momentum · circular motion · newton second law
1.189	Angular Momentum Seen from a Sliding Frame	Difficulty 3 of 5	Uniqueness 4 of 5	angular momentum · frames of reference · relative motion
1.190	A Straight Line Looks Like a Spiral	Difficulty 4 of 5	Uniqueness 5 of 5	angular momentum · non inertial frame · frames of reference
1.191	The Mass Hiding in Two Turning Points	Difficulty 3 of 5	Uniqueness 3 of 5	angular momentum · energy conservation · potential energy
1.192	Sideways Push Toward a Right Angle	Difficulty 4 of 5	Uniqueness 4 of 5	angular momentum · energy conservation · potential energy
1.193	Reeling a Body Toward Its Own Hole	Difficulty 3 of 5	Uniqueness 3 of 5	angular momentum · newton second law · circular motion
1.194	The Torque That Never Needs the Inertia	Difficulty 2 of 5	Uniqueness 3 of 5	angular momentum · torque · constraints pulleys
1.195	Normal and Weight Torques Quietly Cancel	Difficulty 3 of 5	Uniqueness 4 of 5	angular momentum · torque · rolling · limiting cases
1.196	Angular Momentum Shifts with the Origin	Difficulty 2 of 5	Uniqueness 2 of 5	angular momentum · vector decomposition · center of mass
1.197	Angular Momentum, Split at the Center	Difficulty 3 of 5	Uniqueness 3 of 5	angular momentum · center of mass · vector decomposition
1.198	Only the Struck Sphere Feels the Impulse	Difficulty 3 of 5	Uniqueness 3 of 5	momentum conservation · angular momentum · collisions · center of mass
1.199	A Grazing Kick Sets Off a Radial Wobble	Difficulty 4 of 5	Uniqueness 4 of 5	center of mass · angular momentum · energy conservation · approximation expansion