1.
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?

2.
Consider
a yo-yo with its string wound up, ready for action. Suppose that we know nothing about this yo-yo except that it
has the shape of a thin cylinder, with the string wrapped around the outside of
the cylinder. (So this is even
simpler than a regular yo-yo.) If
you release the yo-yo from rest, the string will unwind and it will accelerate
downward, but at what rate?

(a)
Make a
free-body diagram and choose a convenient coordinate system for the yo-yo as it
falls.

(b)
Apply
Newton's 2nd Law (SF = ma) to your FBD. Assuming that the yo-yoÕs mass and radius are known quantities,
can you determine the acceleration of the yo-yo in terms of known quantities
from this equation? Why or why
not?

(c)
Now
choose a rotational coordinate system and apply the torque equation to the
yo-yo (the moment of inertia of a disk is MR^{2}).

(d)
What
is the relationship between *a* (the angular acceleration of the
yo-yo) and *a*
(the linear acceleration of the yo-yo)?

(e)
Using
the results of (b), (c) and (d), determine the acceleration of the yo-yo. Does the answer depend on the mass or
radius of the yo-yo? What *does* it depend on?

(f)
What
is the tension in the string as the yo-yo falls? Give your answer as some fraction or multiple of the weight
of the yo-yo.

3.
Below
is a figure that* *shows
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!

4.
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-m^{2}.

(a)
What
is the acceleration of the block down the plane?

(b)
What
is the tension in the string?