Dynamics
Sample problem: A grindstone with a radius of 0.61 m is being used to
sharpen an ax. If the linear speed of the stone relative to the ax is 1.5 m/s
and its mass is 57 kg, how much heat will be generated after the stone finally
stops spinning?
Solution: The rotational kinetic is completely transformed into heat.
Sample problem: This massive shield door at a neutron test facility at
Lawrence Livermore Laboratory is possibly the world's heaviest hinged door. The
door has a mass of 44,000 kg, a rotational inertia about a vertical axis through
its huge hinges of 8.7x104 kg·m2, and a (front) face width
of 2.4 m. Neglecting friction, what steady force, applied at its outer edge and
perpendicular to the plane of the door, can move it from rest through an angle
of 90° in 30 s?
Solution:
Sample problem: A space station is constructed in the shape of a wheel
114 m in diameter, with essentially all of its 5.5x105 kg mass at the
rim. Once the station is completed, it is set rotating at a rate that requires
an object at the rim to have radial acceleration g, thereby simulating Earth's
surface gravity. This is accomplished using two small rockets, each with 110 N
thrust, that are mounted on the rim of the station as shown. How long will it
take to reach the desired spin rate?
Solution:
Angular Momentum
Sample problem: A child runs with a velocity of 5 m/s tangential to the
rim of a stationary disk-shaped merry-go-round, which has a mass of 250 kg and a
radius of 2.3 m. If the merry-go-round spins at a rate of 6 rpm after the child
jumps on, what is the child’s mass? What percentage of the child’s initial
kinetic energy is lost in the collision?
Solution:
Sample problem: Twin ice skaters, 50 kg each, are moving toward each
other along parallel paths separated by 2.5 m, each at a speed of 10 m/s, and
grab onto a long pole and start spinning. Will they be able to hold on?
Solution:
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