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2D Dynamics
With 2D dynamics, we can explain the orbit of the planets around the Sun, the grandfather clock, and the perfect angle to throw a snowball to nail your nemesis as they run away from you.
Take gravitational acceleration as \( g. \)
Old time mills for grinding wheat or corn into flour were often powered by a water wheel. Some water wheels had water falling over paddles, other water wheels dipped their paddles in a moving river, which as it flowed past turned the wheel. One particular mill has a water wheel with radius \(3~\mbox{m}\) suspended above a river such that the bottom edge of the paddles are just in contact with and move with the river water. If the river flows at \(0.5~\mbox{m/s}\) then what is the period of the spinning water wheel?
A roller coaster works by gravitational energy. The coaster car is pulled up to a high point and then released, rolling downwards on the track through all manners of curves and loops. I have a short roller coaster car that I pull up to the top of a hill of height \(H\). The coaster car is released from this height and must go around a perfectly circular vertical loop with a radius of 20 meters (and the bottom of the loop is on the ground). If I don't want the coaster car to fall off the loop at any point, what should be the minimum value of \(H\) in meters?
Details and assumptions
- Neglect friction and air resistance.
- Treat the roller coaster car as a point.
What is the maximum speed with which a \( 1600 \text{ kg} \) car can make a left turn around a curve of radius \( 49 \text{ m} \) on a level (unbanked) road without sliding?
The static friction constant between the car and the road is \( 0.1, \) and the gravitational acceleration is \( g = 10 \text{ m/s}^2. \)