Motion, forces, energy and momentum, then the vibrations that every rotating machine has to live with.
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With constant acceleration, three equations do almost everything: v = v0 + at, s = v0t + ½at2, and v2 = v02 + 2as.
A car accelerates uniformly from rest to 27 m/s in 9 s. How far does it travel?
a = 3 m/s². s = ½(3)(81) = 122 m. (Or average speed 13.5 × 9.)
Common trap: (C) uses the final speed for the whole time.
KinematicsProjectile Motionconstant accelerationThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Try all of it free for 3 days →
ΣF = ma, applied along each direction of a careful free-body diagram, solves most kinetics problems.
An 800 kg elevator accelerates upward at 2 m/s². What is the cable tension?
T − mg = ma: T = 800(9.81 + 2) = 9,448 N.
Common trap: (C) is the weight alone.
KineticsNewton’s second lawcentripetalThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Try all of it free for 3 days →
Energy methods skip the acceleration entirely: initial energy plus work in equals final energy.
How much power does it take to lift 500 kg at a steady 2 m/s?
P = Fv = mgv = 500(9.81)(2) = 9.8 kW.
WorkKinetic EnergyPotential EnergyPowerThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Try all of it free for 3 days →
Impulse equals change in momentum: FΔt = m(v2 − v1).
A 2,000 kg car at 10 m/s hits a parked 1,000 kg car and they stick together. What is their speed just after impact?
2000(10) = 3000v, so v = 6.67 m/s.
ImpulseMomentumCoefficient of RestitutionThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Try all of it free for 3 days →
For rotation, ΣM = Iα plays the role of F = ma.
A solid disk rolls without slipping down a 30° incline. What is its acceleration?
For a solid disk, a = (2/3)g sin θ = (2/3)(9.81)(0.5) = 3.27 m/s2.
Common trap: (C) is a block sliding without friction.
Rigid BodyMass Moment of InertiaFree VibrationThat was 1 of 3 problems in this section. The full course has the lesson, a worked example and every problem. Try all of it free for 3 days →
Every point on a rigid link moves as if the link were turning about its instant center, so v = rω with r measured from that center.
A four-bar linkage has links of 60, 140, 160 and 200 mm, and the 60 mm link is the fixed frame. What type of linkage is it?
s + l = 60 + 200 = 260 mm ≤ p + q = 140 + 160 = 300 mm, so the linkage is Grashof. With the shortest link fixed, both links pinned to it turn fully: a double-crank (drag link).
Common trap: (A) is the result when the shortest link is next to the frame; here the shortest link is the frame.
Instantaneous CenterRigid Body MotionRelative MotionThat was 1 of 4 problems in this section. The full course has the lesson, a worked example and every problem. Try all of it free for 3 days →
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