A pendulum clock has a rod with a period of 2 s at 20 If the temperature rises to 30 °C, how much does the clock lose or gain in one week? Treat the rod as a physical pendu- lum pivoted at one end. (See Example 15.8.)

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(5.)(1) A pendulum clock has a rod with a period of 2 s at 20 °C.
If the temperature rises to 30 °C, how much does the clock
lose or gain in one week? Treat the rod as a physical pendu-
lum pivoted at one end. (See Example 15.8.)
Transcribed Image Text:(5.)(1) A pendulum clock has a rod with a period of 2 s at 20 °C. If the temperature rises to 30 °C, how much does the clock lose or gain in one week? Treat the rod as a physical pendu- lum pivoted at one end. (See Example 15.8.)
V = L
do
dt
77
= (0.25 m)(0.17) (2m) cos( +
= -0.123 m/s
EXAMPLE 15.8: A uniform rod of mass m and length L is
freely pivoted at one end. (a) What is the period of its oscilla-
tion? (b) What is the length of a simple pendulum with the same
period?
Solution: (a) The moment of inertia of a rod about one end is
I= mL² (Eq. 11.18). The center of mass of a uniform rod is at
its center, so d = L/2 in Eq. 15.17. The period is
2L
3g
T = 2
(b) Comparing Eq. 15.17 with T= 27 VL/g for a simple pendu-
lum, we see that the period of a physical pendulum is the same
as that of an "equivalent" simple pendulum of length
For the uniform rod
Leg
mL²/3
mgL/2
Leq
=
-
I
md
mL²/3
(mL/2)
2п
2L
3
Transcribed Image Text:V = L do dt 77 = (0.25 m)(0.17) (2m) cos( + = -0.123 m/s EXAMPLE 15.8: A uniform rod of mass m and length L is freely pivoted at one end. (a) What is the period of its oscilla- tion? (b) What is the length of a simple pendulum with the same period? Solution: (a) The moment of inertia of a rod about one end is I= mL² (Eq. 11.18). The center of mass of a uniform rod is at its center, so d = L/2 in Eq. 15.17. The period is 2L 3g T = 2 (b) Comparing Eq. 15.17 with T= 27 VL/g for a simple pendu- lum, we see that the period of a physical pendulum is the same as that of an "equivalent" simple pendulum of length For the uniform rod Leg mL²/3 mgL/2 Leq = - I md mL²/3 (mL/2) 2п 2L 3
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