In tightening cylinder-head bolts in an automobile engine, the
critical quantity is the torque applied to the bolts. Why is this more important than the
actual force applied to the wrench handle?
A string is wrapped several times around the rim of a small hoop of radius 0.0800 m and
mass 0.120 kg. If the free end of the string is held in place and the hoop is released
from rest, calculate a) the tension in the string while the hoop descends as the string
unwinds; b) the time it takes the hoop to descend 0.600 m; c) the angular velocity of the
rotating hoop after it has descended 0.600 m.
Below is a figure thatshows three identical yo-yos initially at rest on a
horizontal surface. For each yo-yo the string is pulled in the direction shown. In each
case there is sufficient friction for the yo-yo to roll without slipping. Split into three
groups. Each group should draw the free-body diagram for one of the yo-yo's and convince
themselves and the other two groups that they know the direction the chosen yo-yo will
rotate. If someone in the group reads this ahead of time and brings a yo-yo to workshop it
might help!
A block with mass m=5.00 kg slides down a surface inclined 36.9 degrees to the
horizontal (see the figure below). The coefficient of kinetic friction is 0.25. A string
attached to the block is wrapped around a flywheel on a fixed axis through its center. The
flywheel has mass 20.0 kg, radius R=0.200 m, and a moment of inertia with respect to the
axis 0.400 kg-m2. a) What is the acceleration of the block down the plane? b)
What is the tension in the string?
Each member of the workshop should make up a "cross-product problem" by
drawing two vectors (A and B) oriented somehow in 3 dimensions. The rest of the workshop
should figure out the direction of AxB. Try to be tricky. (It's fair to put vectors at
angles and in and out of the board or give them a magnitude of zero!) Do the same thing
for forces applied at different points to rotating objects (already have an angular
velocity … which might be zero). The rest of the workshop should be able to tell you
the direction of the torque as well as the direction of the angular velocity and angular
acceleration vectors.
