Calculating Rotational Kinetic Energy of a Clock's Hands

In summary, the problem involves finding the total rotational kinetic energy of a clock with an hour hand of 2.7m and a minute hand of 4.5m, assuming they act as long thin rods. The correct equation to use is K=I*rotation vel.^2, where I=(1/3) ML^2. After finding the rotational velocities and converting them to rads/sec, the correct answer is found by plugging in the numbers for the K equation, including squaring the rotational velocities. The mistake in the given solution was not accounting for the 1/2 in the kinetic energy equation.
  • #1
elkedoring
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[SOLVED] Energy in Rotational Motion

There is a clock that has an hour hand 2.7m long with a mass of 60 kg. The minute hand is 4.5m log with a mass of 100 kg. What is the total rotational kinetic energy assuming the hands act as long thin rods?



K=I*rotation vel.^2
I=(1/3) ML^2 ( I think this is the right equation to use)



Ok so first I found the rotational velocities. The minute hand move 1 rev./60min and the hour hand moves 1rev/12hrs. Next I converted them into rads/sec. giving a rotational velocity of .000145444 rads/sec for the first one and .001745329 rads/sec on the second.
Then I went back and plugged in all the numbers for the K equation. [(1/3)*60*2.7^2*.000145444] + [(1/3)*100*4.5^2*.001745329]. This gave me an answer of .00206. This answer is about double what the answer should be (.00103). The only place I thik I may have gone wrong is at the (1/3). Should it (1/6) because the rods are pivoting in between the center of mass (which would use (1/12)) and the end (which is the (1/3) that I used)? Could someone please help me see where I went wrong?
 
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  • #2
At first glance, I noticed you did not square your rotational velocities.
 
  • #3
Rotational kinetic energy is [tex]\frac{1}{2}[/tex]*[tex]I[/tex]*[tex]\omega^{2}[/tex], so I think that's where you're getting twice the intended answer.
 
  • #4
Thank you! I hadn't taken the 1/2 into consideration! That solves it!
 

What is rotational energy?

Rotational energy is the energy that an object possesses due to its rotational motion. It is a form of kinetic energy and is dependent on the object's moment of inertia and angular velocity.

How is rotational energy calculated?

Rotational energy can be calculated using the formula E = 1/2 * I * ω^2, where E is the rotational energy, I is the moment of inertia, and ω is the angular velocity. The moment of inertia is a measure of an object's resistance to changes in its rotational motion.

What is the conservation of rotational energy?

The conservation of rotational energy states that the total amount of rotational energy in a system remains constant, as long as there are no external forces acting on the system. This means that rotational energy can be transformed from one form to another, but the total amount remains the same.

How does rotational energy relate to work and power?

Rotational energy is closely related to work and power in that it can be calculated using the same formulas. Work is the transfer of energy to an object, and in rotational motion, work is done when a torque is applied to an object, causing it to rotate. Power is the rate at which work is done, and in rotational motion, it is the rate at which rotational energy is transferred.

What are some real-life examples of rotational energy?

Some examples of rotational energy in daily life include a spinning top, a spinning bicycle wheel, and a merry-go-round. Other examples include the rotational energy of a car's wheels as it moves, the rotational energy of a wind turbine, and the rotational energy of a planet as it orbits the sun.

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