DYN:010117Cable x+2y=C with vx=3 and ax=-2 forces vy=-3/2 m/s and ay=1 m/s2Dynamics Constraint First DerivativeDynamics Constraint Second DerivativeParticle kinematics in multiple coordinatesEngineering Dynamics · Mixed review—
DYN:010118Collar absolute velocity is (5,0); five-term acceleration is (-1,17.5)Dynamics Relative Velocity Rotating FrameDynamics Five Term AccelerationParticle kinematics in multiple coordinatesEngineering Dynamics · Mixed review—
DYN:010132Helix r=(3cos2t,3sin2t,4t) has speed 2sqrt13; at t=0 the Frenet data are T=(0,3/sqrt13,2/sqrt13), N=(-1,0,0), B=(0,-2/sqrt13,3/sqrt13), kappa=3/13, tau=2/13, at=0, an=12Dynamics Helix Speed From ParametrizationDynamics Frenet Trihedron Curvature TorsionParticle kinematics in multiple coordinatesEngineering Dynamics · Mixed review—
DYN:010133Relative path (6-2t,-2+t) is closest at t=14/5 with offset (2/5,4/5), distance 2/sqrt5, and vanishing dot productDynamics Relative Linear MotionDynamics Closest Approach OrthogonalityParticle kinematics in multiple coordinatesEngineering Dynamics · Mixed review—
DYN:010134Mathematical problem titleDynamics Parabola Plane IntersectionDynamics Plane Tangent Normal ResolutionParticle kinematics in multiple coordinatesEngineering Dynamics · Mixed review—
DYN:010219B descends; a=g(2-sqrt3)/14 and T=3g(12+sqrt3)/14 after a motion auditDynamics Kinetic Friction InclineDynamics Motion Assumption AuditParticle force-acceleration methodsEngineering Dynamics · Mixed review—
DYN:010220Mathematical problem titleDynamics Polar Acceleration ComponentsDynamics Slot Reaction VS ActuatorParticle force-acceleration methodsEngineering Dynamics · Mixed review—
DYN:010235Conical pendulum m=2, L=2, g=10, theta=60 deg has radius sqrt3, T=40 N, speed sqrt30, rate sqrt10, period 2pi/sqrt10Dynamics Conical Vertical Horizontal SplitDynamics Cone Radius Rate PeriodParticle force-acceleration methodsEngineering Dynamics · Mixed review—
DYN:010236Hoop R=2, Omega=sqrt10, g=10 holds a bead at cosθ=1/2 from downward; radius sqrt3, centripetal 10sqrt3, reaction 20 from 10sqrt3 inward and 10 upDynamics Spinning Hoop Effective PotentialDynamics Hoop Reaction From Circular DemandParticle force-acceleration methodsEngineering Dynamics · Mixed review—
DYN:010237Frictionless bank tanθ=3/4 yields N=25 N and v=5sqrt6 m/sDynamics Banked Normal ResolutionDynamics Frictionless Design SpeedParticle force-acceleration methodsEngineering Dynamics · Mixed review—
DYN:010321Elevator shaft output is 40.68 kW; supplied input at eta=0.8 is 50.85 kWDynamics Cable Tension From AccelerationDynamics Mechanical VS Input PowerWork-energy and impulse-momentumEngineering Dynamics · Mixed review—
DYN:010322The impulse (12,8) N s sends vf to (6,5/3) m/s and does 152/3 J of workDynamics Vector Impulse IntegralDynamics Work Energy Variable ForceWork-energy and impulse-momentumEngineering Dynamics · Mixed review—
DYN:010323Mathematical problem titleDynamics Position Force Work IntegralDynamics Instantaneous Power PotentialWork-energy and impulse-momentumEngineering Dynamics · Mixed review—
DYN:010338Central pull keeps H=12, raises vθ from 3 to 6, and does 27 JDynamics Central Angular MomentumDynamics String Work From KineticWork-energy and impulse-momentumEngineering Dynamics · Mixed review—
DYN:010339Inner-loop contact needs hmin=5R/2; at h=3R the top normal is mgDynamics Loop Leave Contact ThresholdDynamics Energy TO Top NormalWork-energy and impulse-momentumEngineering Dynamics · Mixed review—
DYN:010424Rigid kinematics give vB=(-2,2+3sqrt3) and aB=(1-9sqrt3,-6-2sqrt3)Dynamics Rigid Relative VelocityDynamics Rigid Relative AccelerationPlanar rigid-body kinematicsEngineering Dynamics · Mixed review—
DYN:010425Mathematical problem titleDynamics External Gear RatioDynamics Pinion Rack Tangential MatchPlanar rigid-body kinematicsEngineering Dynamics · Mixed review—
DYN:010440Slider-crank at θ=π/2 has x=sqrt3, vx=-2, and ax=4/sqrt3Dynamics Holonomic Slider DerivativesDynamics Theta TO Time AccelerationPlanar rigid-body kinematicsEngineering Dynamics · Mixed review—
DYN:010441Guided coupler gives vC=(8,0) and aC=(-154/3,0) by vector kinematicsDynamics Guided Link Vector VelocityDynamics Guided Link Vector AccelerationPlanar rigid-body kinematicsEngineering Dynamics · Mixed review—
DYN:010442Slot constraint at (3,4) forces ydot=-3/2 and yddot=-13/16; floor-angle omega=-1/2 and alpha=1/16Dynamics Slot Constraint Second DerivativeDynamics Floor Angle Rigid RodPlanar rigid-body kinematicsEngineering Dynamics · Mixed review—
DYN:010526Mathematical problem titleDynamics End Pinned Bar InertiaDynamics Release Pin ReactionPlanar rigid-body kineticsEngineering Dynamics · Mixed review—
DYN:010527Angular impulse 8 N m s takes the flywheel from 4 to 52/5 rad/s; the work is 288/5 JDynamics Angular Impulse MomentumDynamics Rotational Work EnergyPlanar rigid-body kineticsEngineering Dynamics · Mixed review—
DYN:010528The free disk reaches v=4 m/s and omega=12 rad/s; translational work 32 J and rotational work 36 J total 68 JDynamics Unconstrained Plane KineticsDynamics Force Couple Work SplitPlanar rigid-body kineticsEngineering Dynamics · Mixed review—
DYN:010543A 12 N offset on the 6 kg square gives aG=2 i, M=-12 k, alpha=-3 k, and aP=5 iDynamics Mass Center TranslationDynamics Offset Force SpinPlanar rigid-body kineticsEngineering Dynamics · Mixed review—