Rotational kinematics of analog clock

In summary, the question is asking for the number of minutes that elapse before the minute hand and hour hand on an analog clock are pointing in the same direction again, given that at 10:00 the hour hand is 300 degrees ahead of the minute hand. The solution involves creating equations for the motion of the hands and finding the next time where the hands are on top of each other.
  • #1
Chrisleo13
28
0
When it is 10:00, the hour hand on an analog clock is 300 ahead of the minute hand. How many minutes elapse (to three significant digits) before the minute hand next points in the same direction as the hour hand?


I seems really easy, but for some reason I am not getting the right answer.

Can I use rotational kinematics?
 
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  • #2


Chrisleo13 said:
When it is 10:00, the hour hand on an analog clock is 300 ahead of the minute hand. How many minutes elapse (to three significant digits) before the minute hand next points in the same direction as the hour hand?I seems really easy, but for some reason I am not getting the right answer.

Can I use rotational kinematics?

Looks like a logic problem.

Write an equation for the motion of the hands of a clock. What is the speed of the hour hand? What is the speed of the minute hand.

Then figure the next time the hands have the opportunity to be 300 degrees apart again and create an equation that takes into account the effect of both the hand in getting to be exactly 300 degrees apart.
 
  • #3


First of all, think what is the next time after 10.00 where the two hands of a clock are on top of each other? That's essentially your answer - the only time the hands of a clock are pointing in the same direction is when they're on top of one another.
 

1. What is rotational kinematics?

Rotational kinematics is the branch of physics that deals with the motion of objects as they rotate or spin around a fixed axis.

2. How does an analog clock use rotational kinematics?

An analog clock uses rotational kinematics to measure and display time. The hands of the clock rotate around a fixed axis, with each rotation representing a specific unit of time (e.g. one hour).

3. What is the relationship between the seconds, minutes, and hours hand on an analog clock?

The seconds, minutes, and hours hand on an analog clock are all connected to the same axis, but they rotate at different speeds. The seconds hand makes one full rotation every 60 seconds, the minutes hand makes one full rotation every 60 minutes, and the hours hand makes one full rotation every 12 hours.

4. How does an analog clock keep accurate time?

An analog clock keeps accurate time by using a small motor and gears to control the rotation of the hands. The motor is connected to a power source, which provides a constant force to keep the hands moving at the correct speed.

5. Can rotational kinematics be applied to other objects besides analog clocks?

Yes, rotational kinematics can be applied to any object that rotates or spins around a fixed axis, such as a spinning top, a merry-go-round, or a planet orbiting around the sun. It is a fundamental principle in understanding the motion of many natural and man-made systems.

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