Rotational Kinetic Energy of merry-go-round

In summary, a 31.0 kg child with a speed of 2.80 m/s runs tangential to the rim of a stationary merry-go-round with a moment of inertia of 520 kg*m^2 and a radius of 2.51 m. When the child jumps onto the merry-go-round, the system begins to rotate. The initial kinetic energy of the system is 122 J. To calculate the final kinetic energy of the system, conservation of angular momentum can be used to find the angular velocity and then calculate the rotational energy.
  • #1
fleabass123
8
0

Homework Statement



A 31.0 kg child runs with a speed of 2.80 m/s tangential to the rim of a stationary merry-go-round . The merry-go-round has a moment of inertia of 520 kg\cdot m^2 and a radius of 2.51 m. When the child jumps onto the merry-go-round, the entire system begins to rotate.

A) Calculate the initial kinetic energy of the system.

B) Calculate the final kinetic energy of the system.

Homework Equations


E=1/2*m*v^2+1/2*I*w^2


The Attempt at a Solution



I got the answer to part A by simply doing KE=1/2*m*v^2. The answer was 122 J.
I'm not sure how to approach part B, however. I thought that because of conservation of mechanical energy that the initial energy would equal the final and I could use my answer from part A to solve part B. But this isn't working. Any help would be appreciated. :D
 
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  • #2
The KE energy is not the same as it was initially. There must be some interaction between the child and merry-go-round to set it into rotation and this consumes some energy. You can use conservation of angular momentum to calculate angular velocity, and calculate the rotational energy from that.

ehild
 

What is rotational kinetic energy?

Rotational kinetic energy is the energy possessed by an object due to its rotation. It is dependent on the mass, radius, and angular velocity of the object.

How is rotational kinetic energy calculated?

The formula for calculating rotational kinetic energy is KE = 1/2 * I * ω^2, where KE is the kinetic energy, I is the moment of inertia, and ω is the angular velocity.

How does the mass and radius affect the rotational kinetic energy of a merry-go-round?

The mass and radius of a merry-go-round both directly affect its rotational kinetic energy. A larger mass or radius will result in a higher rotational kinetic energy.

How does the angular velocity of a merry-go-round affect its rotational kinetic energy?

The angular velocity of a merry-go-round has a direct relationship with its rotational kinetic energy. As the angular velocity increases, so does the rotational kinetic energy.

Why is rotational kinetic energy important in understanding the motion of a merry-go-round?

Rotational kinetic energy is important in understanding the motion of a merry-go-round because it helps us understand how the object is moving and how much energy is required to keep it in motion. It also allows us to make predictions about the behavior of the object and its stability.

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