DYN:010117Cable x+2y=C with vx=3 and ax=-2 forces vy=-3/2 m/s and ay=1 m/s2View access optionsDynamics 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)View access optionsDynamics 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=12View access optionsDynamics 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 productView access optionsDynamics Relative Linear MotionDynamics Closest Approach OrthogonalityParticle kinematics in multiple coordinatesEngineering Dynamics · Mixed review—
DYN:010134Parabola r=(10t,10t-5t^2) reenters y=x/2 at (10,5); plane travel is 5sqrt5, v=(10,0) splits as 4sqrt5 and -2sqrt5 on (2,1)/sqrt5 and (-1,2)/sqrt5View access optionsDynamics 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 auditView access optionsDynamics Kinetic Friction InclineDynamics Motion Assumption AuditParticle force-acceleration methodsEngineering Dynamics · Mixed review—
DYN:010220At t=1 the polar force is -10 e_r+8 e_theta N; the slot supplies the 8 NView access optionsDynamics 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/sqrt10View access optionsDynamics 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 upView access optionsDynamics 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/sView access optionsDynamics 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 kWView access optionsDynamics 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 workView access optionsDynamics Vector Impulse IntegralDynamics Work Energy Variable ForceWork-energy and impulse-momentumEngineering Dynamics · Mixed review—
DYN:010323The force 6x^2 does 16 J of work; the final power is 24sqrt17 WView access optionsDynamics 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 JView access optionsDynamics 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 mgView access optionsDynamics 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)View access optionsDynamics Rigid Relative VelocityDynamics Rigid Relative AccelerationPlanar rigid-body kinematicsEngineering Dynamics · Mixed review—
DYN:010425External gears send the top rack right at 0.4 m/s and 0.16 m/s^2View access optionsDynamics 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/sqrt3View access optionsDynamics 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 kinematicsView access optionsDynamics 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=1/16View access optionsDynamics Slot Constraint Second DerivativeDynamics Floor Angle Rigid RodPlanar rigid-body kinematicsEngineering Dynamics · Mixed review—
DYN:010526A released pinned bar has alpha=-15/2 rad/s^2 and pin reaction (0,15) NView access optionsDynamics 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 JView access optionsDynamics 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 JView access optionsDynamics 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 iView access optionsDynamics Mass Center TranslationDynamics Offset Force SpinPlanar rigid-body kineticsEngineering Dynamics · Mixed review—