If an hour hand is .01667 rev/s, a minute hand is 2.78e-4 rev/s, what is the second hand rotation speed? I've tried everything and can't get a correct answer.
Thank you
Correction. The Hour Hand is 2.31e-05 rev/s; the Minute Hand is 2.78e-4 rev/s. I've checked with 3 tutors and none of them have gotten an answer that works for the Second Hand rotational speed in rev/s. Thank you
the hour hand makes one revolution each 12 hours, the minutehand makes on rev each 60 min.
speed minute hand=speedhourhand*12
= 2.31E-5*12= 2.78E-4 rev /sec
The second hand makes one rev per min. or
speed second hand=speedminutehand*80
= 2.78E-4 rev/sec* 60= = 0.01668 rev/sec
check: the second hand should rotate one rev in sixtysecond
60*.01668=1 rev
answer key marks that as incorrect.
thanks though
To find the rotation speed of the second hand, we first need to understand the relationship between the three hands of a clock. In a standard clock, the second hand completes one revolution (360 degrees) in 60 seconds.
Given that the hour hand is rotating at a speed of 0.01667 revolutions per second and the minute hand at a speed of 2.78e-4 revolutions per second, we can calculate the number of revolutions the second hand completes in one second.
To do this, we need to determine the relative speeds of the hour and minute hands compared to the second hand.
Since the hour hand completes one revolution every 12 hours and there are 60 minutes in an hour, we can calculate its speed in revolutions per second:
Hour hand speed = 1 revolution / (12 hours * 60 minutes * 60 seconds) = 1/43200 revolutions per second.
Similarly, the minute hand completes one revolution every hour, or 60 minutes, which translates to:
Minute hand speed = 1 revolution / (60 minutes * 60 seconds) = 1/3600 revolutions per second.
Now, to find the rotation speed of the second hand, we subtract the speeds of the hour and minute hands from the standard speed of the second hand. Thus:
Second hand speed = 1 revolution per second - (Hour hand speed + Minute hand speed)
Plugging in the values, we get:
Second hand speed = 1 - (1/43200 + 1/3600) revolutions per second
Performing the calculations yields a result of approximately 0.01389 revolutions per second for the rotation speed of the second hand.
Therefore, the rotation speed of the second hand is approximately 0.01389 revolutions per second.