In this paper we derive and discuss the time it takes for a force to turn a velocity. More precisely, we derive the formula for the time τ it takes a constant force that makes an angle α with the initial velocity v(0) to have v(τ) get within an angle θ < α of the force. We then show how the addition of a viscous force decreases τ logarithmically. The result can be generalized to any vector quantity whose first time derivative is a constant.
References
1.
E.
Disy
and J.
Garner
, “Hypothetical pre-classical equations of motion
,” Phys. Teach.
37
, 42
–45
(Jan.
1999
).2.
The rate of change of force is proportional to the “jerk
,” and its interpretation is discussed in Ref. 3.3.
T. R.
Sandin
, “The jerk
,” Phys. Teach.
28
, 36
–40
(Jan.
1990
).4.
This can be found by differentiating Eq. (2) with regard to α and setting to zero to find the critical point. A useful identity is cot θ = tan(π/2 – θ
).5.
R. A.
Serway
and J. W.
Jewett
Jr., Physics for Scientists and Engineers, Annotated Instructor’s
9th ed. (Brooks/Cole
, Boston
, 2014
), p. 764
.6.
R.
Cross
, “Standing, walking, running, and jumping on a force plate
,” Am. J. Phys.
67
, 304
–309
(April
1999
).7.
E. M.
Purcell
, “Life at low Reynolds number
,” Am. J. Phys.
45
, 3
–11
(Jan.
1977
).© 2019 American Association of Physics Teachers.
2019
American Association of Physics Teachers
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.