Homework Assignment 12

Homework Assignment 12
Problem 1
A particle with mass 2.13 kg has position ~r and velocity ~v (see picture.) It is acted on
by the force F~ . All three vectors lie in a common plane. Given: r = 2.91m,v = 4.18 ms
and F = 1.88N. compute (a) angular momentum of the particle and (b) torque about
the origin, acting on the particle. What are the directions of these two vectors?
Problem 2
Two skaters, each of mass 51.2 kg. approach each other along parallel paths separated
by 2.02 m. They have equal and opposite velocities of 1.38 m/s. The rst skater carries
a long light pole 2.92 m long, and the second skater grabs the end of it as he passes.
They are on ice with no friction. (a) Describe quantitavely the motion of the skaters
after they are connected by the pole. (b) By pulling on the pole, the skaters reduce
their separation to 0.940 m. Find their angular speed then.
Problem 3
Show that a cylinder will slip on an inclined plane which is at angle θ if the coecient
of static friction between plane and cylinder is less than 13 tanθ.
Problem 4
A pulley with rotational inertia 1.14 × 10−3 kg · m2 and a radius of 9.88cm is acted on
by a force, applied tangentially at its rim, that varies in time as F = At + Bt2 . Given:
A = 0.496 Ns and B = 0.305 sN2 . If the pulley was initially at rest, nd its angular speed
after 3.60 seconds.
Problem 5
A man stands on a platform that is rotating with an angular speed of 1.22 rev/s.
His arms are stretched out and he holds a weight in each hand. With his hands in
this position the total rotational inertia of the man, the weigths, and the platform is
6.13kg · m2. . Then the man moves the weights so that the rotational inertia is now
1.97kg · m2. . (a) What is the resulting angular speed of the platform? (b) What is the
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ratio of the new kinetic energy to the original kinetic energy? (The platform rotates
without friction).
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