A cycloid is the curve traced by a point on a circle as it rolls along a straight line without slipping. Find the Lagrangian for a particle of mass m constrained to a single arc of a cycloid associated with a forward-rolling circle of radius r in a uniform gravitational field (with a gravitational acceleration g directed vertically downward).

When using the ohmmeter function of a digital multimeter, the leads are placed in what position relative to the component being tested? a. parallel b. control c. series d. line

Ariver flows from north to south at 8 km/h. a boat is to cross this river from west to east at a speed of 20 km/h (speed of the boat with respect to the earth/ground). at what angle (in degrees) must the boat be pointed upstream such that it will proceed directly across the river (hint: find the speed of the boat with respect to water/river)? a 288 b. 21.8 c. 326 d. 30.2

Ajournal bearing has a journal diameter of 3.250 in with a unilateral tolerance of 20.003 in. the bushing bore has a diameter of 3.256 in and a unilateral tolerance of 0.004 in. the bushing is 2.8 in long and supports a 700-lbf load. the journal speed is 900 rev/min. find the minimum oil film thickness and the maximum film pressure for both sae 20 and sae 20w-30 lubricants, for the tightest assembly if the operating film temperature is 160°f. a computer code is appropriate for solving this problem.