One can simply find the frictional force acting on an object using this equation:
(Ffrict<span> = μ•F</span>norm<span>)
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The process of determining the value of the individual forces acting upon an object involve an application of Newton's second law (Fnet=m•a) and an application of the meaning of the net force. If mass (m) and acceleration (a) are known, then the net force (Fnet) can be determined by use of the equation.
<span>Fnet = m • a</span>
If the numerical value for the net force and the direction of the net force is known, then the value of all individual forces can be determined.
Apply conservation of angular momentum:
L = Iw = const.
L = angular momentum, I = moment of inertia, w = angular velocity, L must stay constant.
L must stay the same before and after the professor brings the dumbbells closer to himself.
His initial angular velocity is 2π radians divided by 2.0 seconds, or π rad/s. His initial moment of inertia is 3.0kg•m^2
His final moment of inertia is 2.2kg•m^2.
Calculate the initial angular velocity:
L = 3.0π
Final angular velocity:
L = 2.2w
Set the initial and final angular momentum equal to each other and solve for the final angular velocity w:
3.0π = 2.2w
w = 1.4π rad/s
The rotational energy is given by:
KE = 0.5Iw^2
Initial rotational energy:
KE = 0.5(3.0)(π)^2 = 14.8J
Final rotational energy:
KE = 0.5(2.2)(1.4)^2 = 21.3J
There is an increase in rotational energy. Where did this energy come from? It came from changing the moment of inertia. The professor had to exert a radially inward force to pull in the dumbbells, doing work that increases his rotational energy.
The transfer of heat that utilizes or occurs in the form of wave, would be B. Radiation. As heat, can be emitted in the form of waves which constitute or make up the electromagnetic spectrum, specifically these include UV Rays from the sun for instance.
