Rotating bodies and angular momentum : Rolling objects and moment of inertia
A sphere of radius mass M and moment of inertia I rolls down a slope that is inclined at an angle phi to the horizontal. The sphere starts from rest and rolls without slipping a distance L down the slope. Choose coordinates x and theta as shown. a) Write down a relationship between x and theta. Please see the attached fi ...continues
Rotating bodies and angular momentum - rolling objects
I have answers for (a) and (b) but (c) is elluding me! Please shed some light on this supposedly simple problem concerning an object rolling down a slope! See attached file for full problem description. Thank you
Parametric/simultaneous equations and matrices.
See attached file for full problem description with diagrams and equations --- Parametric equations and matrices. The diagram below shows a line defined by the parametric equations , which crosses the x- and y-axes at the points (a, 0) and (0, b), respectively. The region marked A, is bounded by this line, the x- axes, th ...continues
Objects sliding down a rough plane...
I have calculated an answer (D), but am not totally sure about its accuracy. Please could you work out the correct answer so I can compare. (See attached file for full problem description)
Equation of motion of two springs
I think the answer is A but could you confirm (or correct) my calculations. (See attached file for full problem description)
What is the energy stored in the two springs? (See attached file for full problem description)
Forming relationships between variables
Please help! I cannot seem to get this problem solved! (See attached file for full problem description)
A plane flying with a constant speed of 24 km/min passes over a ground radar station at an altitude of 9 km and climbs at an angle of 40 degrees. At what rate is the distance from the plane to the radar station increasing 3 minutes later?
Mathematical modeling using systems of linear first order equations
Two tanks each hold 3 liters of salt water and are connected by two pipes (see figure below) the salt water in each tank is kept well stirred. Pure water flows into tank A at a rate of 5 liters per minute and the salt mixture exits tank B at the same rate. Salt water flows from tank A to tank B at the rate of 9 liters per min ...continues
Simulation using Crystal Ball / OptQuest
This problem requires the use "Crystal Ball", the popular commercial spreadsheet add-in. For clarity, it is distributed by Decisioneering, Inc. This problem specifically requires that Excel and "Crystal Ball" (and OptQuest as applicable) be used - and not any other software choices. The link below directs you to a free 7-day t ...continues
