Question 22 - Problems - Chapter 2

Problem:

On a particular wristwatch, the tips of the minute and second hands are each 0.90 cm from the center, whereas the tip of the hour hand is 0.50 cm from the center.

Question:

What is the average speed of each of these three tips?

Solution:

The distance the tip of the second- and minutehand is traveling is the circumference of a circle.

Distance minute and second $s_{ms} = 2.\pi.r$ where $r=9.0mm$

Distance hour hand is $s_h = 2.\pi.r$ where $r=5.0mm$

The time to travel the wole circle is

Time second hand $t_s = 1$ min.

Time minute hand $t_m = 1$ hour.

Time hour hand $t_h = 12$ hours.

import numpy as np
import pint
u = pint.UnitRegistry()
r_ms = 9 * u.mm
r_h = 5 * u.mm
s_ms = 2 * np.pi * r_ms
s_h = 2 * np.pi * r_h
t_s = 1 * u.min
t_m = 1 *u.hour
t_h = 12 * u.hour
Speed_s = s_ms / t_s
Speed_m = s_ms / t_m
Speed_h = s_h / t_h
print(f'- the average speed of the second hand is {Speed_s.to(u.m / u.s):.2e}.')
print(f'- the average speed of the minute hand is {Speed_m.to(u.m / u.s):.2e}.')
print(f'- the average speed of the hour hand is {Speed_h.to(u.m / u.s):.2e}.')

- the average speed of the second hand is 9.42e-04 meter / second.
- the average speed of the minute hand is 1.57e-05 meter / second.
- the average speed of the hour hand is 7.27e-07 meter / second.