Angular velocity- pendulums and ideal springs

In summary, to determine whether a room is on Earth or on the moon if you are held prisoner by space invaders, you can use a watch and a pair of shoes with shoelaces to calculate the angular frequency. By comparing the calculated frequency to the Earth's value and timing the pendulum for multiple cycles, you can determine if you are on Earth or not. It is recommended to use a smaller angle to get a more accurate result.
  • #1
chantalprince
54
0

Homework Statement



Suppose you were kidnapped and held prisoner by space invaders in a completely isolated room, with nothing but a watch and a pair of shoes (with shoelaces of known length). Explain how you might determine whether this room is on Earth or on the moon.

Homework Equations



ang. velocity (W) = square root of (g/L)

W= 2 pi (f)


The Attempt at a Solution



Ok- I know that gravity is less on the moon than here on earth, so the frequency would be slower. I know that this has something to do with comparing frequency's of the watch and of a pendulum (dangling shoes or watch (?) from shoelaces) but I'm not making the connection on how a person would do this.
 
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  • #2
Insert the value for gearth and calculate the what the angular frequency would be (hope you have a pencil in your pocket). Find the period of one cycle from the angular frequency. Construct the boot pendulum with length L, pull the boot about 10 degrees off the vertical and release. Use the watch and time ten cycles. Divide by 10 to give the time for one cycle. If this time agrees with the Earth calculation then you didn't leave the earth.
 
  • #3
Why 10 degrees? I know all of this relates back to the angle that the path swings out somehow. Would it be the same if I did say, a 45 degree angle (easier to meausre) and then counted 45 cycles and divided by 45? What does the angle have to do with it??
 
  • #4
The equation you are using to determine the angular frequency is for small angles of less than 15 degrees. For larger angles the math is much more complicated to solve the equation of motion and the angular frequency equation becomes dependent on the starting angle which you can't measure unless you walk around all the time with a protractor! Timing for 10 cycles has nothing to do with starting the boot at 10 degrees. I suggested 10 cycles to get a reliable value for the period. You could time for more cylces like 45 then divide by 45 and you will still get the time for one cycle but it would be a little more accurate than timing 10 cycles.
 
  • #5
Awesome- very helpful! Thanks so much.
 

FAQ: Angular velocity- pendulums and ideal springs

What is angular velocity?

Angular velocity is a measure of how fast an object is rotating around a fixed point. It is usually represented by the Greek letter omega (ω) and is measured in radians per second.

How is angular velocity related to pendulums?

In pendulum motion, the angular velocity is directly proportional to the length of the pendulum and the force of gravity acting on it. As the pendulum swings back and forth, the angular velocity changes, reaching its maximum at the bottom of the swing and decreasing to zero at the highest points.

What is the relationship between angular velocity and ideal springs?

Ideal springs are objects that follow Hooke's law, which states that the force exerted by a spring is directly proportional to the displacement of the spring from its equilibrium position. This means that the angular velocity of an ideal spring is also directly proportional to the displacement of the spring.

How does mass affect angular velocity in pendulums and ideal springs?

In a pendulum, the mass does not affect the angular velocity, but it does affect the period of the pendulum. In an ideal spring, the mass does not affect the angular velocity or the period, as long as the spring remains within its elastic limit.

Can angular velocity be negative?

Yes, angular velocity can be negative. This means that the object is rotating in the opposite direction of positive angular velocity. It is important to note that the direction of angular velocity is determined by the direction of rotation and not the magnitude of the velocity.

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