A movie lasts 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
a. 2pi /360 x 60 = 1.04 radians
b. 2pi / 360 x 2 x 360 = 12.56 radians
c. 2pi / 360 x 120 x 360 = 753.98 radians
a. Oh, the poor hour hand must be feeling a little sluggish! In 2 hours, the hour hand completes a full 360-degree rotation. It's taking its sweet time, but it eventually gets there.
b. Ah, the minute hand! It's a speed demon compared to the hour hand. In 2 hours, the minute hand covers a total angular displacement of 720 degrees. Zooming around the clock like it's in a rush!
c. Brace yourself for this one! The second hand is a whirlwind of activity during a movie. In just 2 hours, it completes a staggering 43,200-degree rotation. It's like watching a marathon runner on fast-forward!
To find the angular displacement of each hand in a 2-hour movie, we need to determine how much each hand moves in one second.
a. The hour hand:
In most analog clocks, the hour hand completes a full rotation of 360 degrees in 12 hours (or 720 minutes, or 43,200 seconds). Therefore, in one second, the hour hand will move 360 degrees divided by 43,200 seconds, which equals 0.00833 degrees.
So, during a 2-hour movie, the hour hand will move 0.00833 degrees per second multiplied by 43,200 seconds (for two hours), which equals 360 degrees.
b. The minute hand:
In most analog clocks, the minute hand completes a full rotation of 360 degrees in 60 minutes (or 3,600 seconds). Therefore, in one second, the minute hand will move 360 degrees divided by 3,600 seconds, which equals 0.1 degrees.
So, during a 2-hour movie, the minute hand will move 0.1 degrees per second multiplied by 43,200 seconds (for two hours), which equals 4,320 degrees.
c. The second hand:
In most analog clocks, the second hand completes a full rotation of 360 degrees in 60 seconds. Therefore, in one second, the second hand will move 360/60 = 6 degrees.
So, during a 2-hour movie, the second hand will move 6 degrees per second multiplied by 43,200 seconds (for two hours), which equals 259,200 degrees.
To summarize:
a. The hour hand will move 360 degrees during a 2-hour movie.
b. The minute hand will move 4,320 degrees during a 2-hour movie.
c. The second hand will move 259,200 degrees during a 2-hour movie.
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a. 30o/h *2h = 60o.
b. 360o/h * 2h = 720o.
c. 4320o/h * 2h = 8640o