The stereotypical situation of a snowball picking up both mass and speed as it rolls without slipping down a hill provides an opportunity to explore the general form of both translational and rotational versions of Newton’s second law through multivariable differential equations. With a few reasonable assumptions, it can be shown that the snowball reaches a terminal acceleration. While the model may not be completely physically accurate, the exercise and the resulting equation are useful and accessible to students in a second year physics course, arguably.

1.
John
Mallinckrodt
, “
F does not equal d(mv)/dt
,”
Phys. Teach.
48
,
360
(
Sept.
2010
).
2.
Martin
Tiersten
, “
Force, momentum change, and motion
,”
Am. J. Phys.
37
,
82
22
(
Jan.
1969
).
3.
J.
Matolyak
and
G.
Matous
, “
Simple variable mass systems: Newton’s second law
,”
Phys. Teach
.
28
,
328
329
(
May
1990
).
4.
K. S.
Krane
, “
The falling raindrop: Variations on a theme of Newton
,”
Am. J. Phys
.
49
,
113
117
(
Feb.
1981
).
5.
Alan D.
Sokal
, “
The falling raindrop, revisited
,”
Am. J. Phys
.
78
,
643
644
(
June
2010
).
6.
Carl E.
Mungan
, “
More about the falling raindrop
,”
Am. J. Phys
.
78
,
1421
1424
(
Dec.
2010
).
7.
B. G.
Dick
, “
On the raindrop problem
,”
Am. J. Phys
.
54
,
852
854
(
Sept.
1986
).
AAPT members receive access to The Physics Teacher and the American Journal of Physics as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.