Ch8_2
New Problems
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Make sure to calculate your answers in SI units unless specified otherwise .
1) A
kg
object (neglect its size) is held by a rod a distance of
m
from the axis of rotation and moves on a circular orbit when pushed. What is the moment of inertia of the object
(see sheet 16,17
) ? Indicate with a positive (negative) sign whether the moment of inertia of this object increases by a factor 3 (9) when its distance to the axis of rotation is tripled.
2) A
kg
uniform disk turns about an axis of rotation through its center which is perpendicular to the disk plane. The disk has a moment of inertia of
kgm
2
. What is the diameter of the disk
(see sheet 18)
? Indicate with a positive (negative) sign whether the moment of inertia with respect to an axis with the same direction but placed at the rim of the disk is smaller (larger) than for the axis in the center.
3) A mass
m
=
kg
hangs from a
kg
uniform disk via a string which is wound around the circumference of the disk
(see sheet 21
with no counter weight on the left hand side
)
. After you release the mass it accelerates downward. (Assume that the the string does not slip while unwinding from the disk). What is the linear acceleration of the mass ?
(see sheet 23
on how to express the torque due to
m
in terms of the linear acceleration, then relate this net torque to the angular acceleration as on
sheet 22
; relate the angular acceleration to the linear one and solve for it; the moment of inertia is given on
sheet 18
; note that the radius of the disk drops out in the final expression for the linear acceleration)
4) A uniform
kg
sphere
(
the factor f=2/5 on
sheet 18)
with a
cm
radius spins at
rpm
. What is the angular momentum of the sphere
(see sheet 26)
. Indicate with a negative (positive) sign whether the angular momentum stays the same (changes) in the absence of any torque acting on the sphere.
5) A diver makes a series of summersaults during a diving competition. Stretched out he rotates about an axis which is horizontal and perpendicular to his body. He then goes into a tuck reducing his moment of inertia by a factor of making now revolutions per second. What was his initial angular velocity in revolutions per second
(see sheet 27)
. Indicate with a negative (positive) sign whether inclusion of air resistance and thus inclusion of an external torque would (not) modify your answer.
6) Use the model for a
kg
person bending over and holding a weight while the torso is in a horizontal position given on
sheet 42,45'
. The weight held has a
kg
mass and has a horizontal distance
L
from the hip joint (the pivot point). The torso, head and arms taken together (modeled by the ruler) is 65% of the body weight with a center of mass point at a distance of about
L
away from the hip. Assume that the point of action for the various back muscles holding the torso in the horizontal position (modeled by the cable) is a distance 0.45
L
from the hip. What is the tension of "the" backmuscle which makes a 12
0
degree
angle with the horizontal
(see sheet 43,44 top)
? Indicate with a negative (positive) sign whether the tension is larger (smaller) than the body weight.
Once you have submitted your answers for grading by clicking the grade button, you
cannot resubmit answers
for the same Problem Set--you must use the 'New Problems' button first.