a movie last 2 hours. during that time what is the angular displacement of each of the following? a.the hour hand b.the minute hand c.the second hand
hour hand goes 2/12 * 2PI radians
minute hand= 120*2PI
second= minute displacement*60
check my thinking.
To calculate the angular displacement of each hand on a clock during a 2-hour movie, we need to know the angular speed of each hand and the total time in hours.
a. The hour hand: The hour hand completes a full rotation every 12 hours (720 minutes) since there are 12 divisions on the clock face. Therefore, the angular speed of the hour hand can be calculated by dividing 360 degrees by 720 minutes, which is 0.5 degrees per minute.
For a 2-hour movie, the time is 120 minutes. Therefore, the angular displacement of the hour hand can be calculated by multiplying the angular speed (0.5 degrees per minute) by the total time (120 minutes):
Angular Displacement of Hour Hand = Angular Speed x Total Time
Angular Displacement of Hour Hand = 0.5 degrees per minute x 120 minutes
Angular Displacement of Hour Hand = 60 degrees
So, the hour hand would have an angular displacement of 60 degrees.
b. The minute hand: The minute hand completes a full rotation every 60 minutes (3600 seconds) since there are 60 divisions on the clock face. Therefore, the angular speed of the minute hand can be calculated by dividing 360 degrees by 3600 seconds, which is 0.1 degrees per second.
For a 2-hour movie, the time is 120 minutes (7200 seconds). Therefore, the angular displacement of the minute hand can be calculated by multiplying the angular speed (0.1 degrees per second) by the total time (7200 seconds):
Angular Displacement of Minute Hand = Angular Speed x Total Time
Angular Displacement of Minute Hand = 0.1 degrees per second x 7200 seconds
Angular Displacement of Minute Hand = 720 degrees
So, the minute hand would have an angular displacement of 720 degrees.
c. The second hand: The second hand completes a full rotation every 60 seconds. Therefore, the angular speed of the second hand is 360 degrees per minute.
For a 2-hour movie, the time is 120 minutes (7200 seconds). Therefore, the angular displacement of the second hand can be calculated by multiplying the angular speed (360 degrees per minute) by the total time (7200 seconds):
Angular Displacement of Second Hand = Angular Speed x Total Time
Angular Displacement of Second Hand = 360 degrees per minute x 7200 seconds
Angular Displacement of Second Hand = 2,592,000 degrees
So, the second hand would have an angular displacement of 2,592,000 degrees.
To calculate the angular displacement of each hand of a clock during a given period of time, you need to know the time increment covered by one complete revolution of each hand.
a. The hour hand completes one full revolution in 12 hours. Therefore, to find the angular displacement for 2 hours, you need to divide 2 by 12 and multiply by 360 degrees:
Angular displacement of the hour hand = (2/12) * 360 = 60 degrees
b. The minute hand completes a revolution in 60 minutes. As there are 60 minutes in an hour, the minute hand takes 60 minutes to move 360 degrees, or 6 degrees per minute:
Angular displacement of the minute hand = 2 hours * 60 minutes * 6 degrees per minute = 720 degrees
c. The second hand completes one revolution in 60 seconds, which translates to 6 degrees per second:
Angular displacement of the second hand = 2 hours * 60 minutes * 60 seconds * 6 degrees per second = 43,200 degrees
Therefore, the angular displacement of each hand during a 2-hour movie would be:
a. 60 degrees for the hour hand
b. 720 degrees for the minute hand
c. 43,200 degrees for the second hand