Displacement Vector of Minute Hand: 8-8:20 & 8-9:00 a.m.

In summary, the displacement vector of the tip of the minute hand from 8:00 to 8:20 a.m. can be expressed as r_x = -0.346 cm, r_y = 1.997 cm. From 8:00 to 9:00 a.m., the displacement vector can be expressed as r_x = 2.0 cm, r_y = 0 cm. To begin solving these problems, you can use the formula \vec r(t) = \hat i L \sin \left( 2 \pi \frac {T}{12} \right) + \hat j L \cos \left( 2 \pi \frac {T}{12} \right), where
  • #1
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The minute hand on a watch is 2.0 cm in length. What is the displacement vector of the tip of the minute hand

From 8:00 to 8:20 a.m.? Express vector r in the form r_x, r_y, where the x and y components are separated by a comma.

and

From 8:00 to 9:00 a.m.? Express vector r in the form r_x, r_y, where the x and y components are separated by a comma.

I am no idea how to do these problems. could someone give some suggestions as to how to begin?
 
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  • #2
[tex]\vec r(t) = \hat i L \sin \left( 2 \pi \frac {T}{12} \right) + \hat j L \cos \left( 2 \pi \frac {T}{12} \right)[/tex]

where L is the length of the minute hand and T is the time measured in hours.
 
  • #3
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Related to Displacement Vector of Minute Hand: 8-8:20 & 8-9:00 a.m.

1. What is the displacement vector of the minute hand between 8:00 and 8:20 a.m.?

The displacement vector of the minute hand between 8:00 and 8:20 a.m. is equal to 1/3 of a full rotation, or 120 degrees clockwise.

2. How do you calculate the displacement vector of the minute hand between 8:00 and 9:00 a.m.?

To calculate the displacement vector of the minute hand between 8:00 and 9:00 a.m., we first need to determine the number of minutes between the two times. In this case, there are 60 minutes between 8:00 and 9:00 a.m. Next, we divide 360 degrees (a full rotation) by 60 minutes to get 6 degrees per minute. Therefore, the displacement vector of the minute hand between 8:00 and 9:00 a.m. is 6 degrees per minute multiplied by 60 minutes, which equals 360 degrees.

3. Is the displacement vector of the minute hand between 8:00 and 8:20 a.m. larger or smaller than the displacement vector between 8:00 and 9:00 a.m.?

The displacement vector of the minute hand between 8:00 and 8:20 a.m. is smaller than the displacement vector between 8:00 and 9:00 a.m., since 8:20 a.m. is closer to the starting position (8:00 a.m.) than 9:00 a.m.

4. Does the displacement vector of the minute hand change if the clock is set to a different time zone?

No, the displacement vector of the minute hand is based on the number of minutes between two given times, regardless of the time zone. The only difference would be the actual time displayed on the clock.

5. Can the displacement vector of the minute hand be negative?

No, the displacement vector of the minute hand is always represented in a positive value, since it is a measure of the angle and direction of rotation from the starting position to the ending position.

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