Differences

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--- 183_notes:pp_vs_real [2021/05/08 19:09] – [Energy in the Real System] stumptyl
+++ 183_notes:pp_vs_real [2021/05/08 19:12] – [An application] stumptyl
@@ Line 50: / Line 50: @@
 In the point particle system, you need information about the net force and the center of mass; the point of application of the net force is the center of mass and it acts through the displacement of the center of mass. From the point particle system, you gain information about the translational kinetic energy of the system only.
-==== An application ====
+===== An Application =====
-This might all seem abstract right now, but consider two pucks with same mass ($m$) that are pulled across an icy surface. Puck 1 has the rope attached to its center and Puck 2 has the rope wound about its edge (see below).
+This might all seem abstract right now, but consider two pucks with the same mass ($m$) that are pulled across an icy surface. Puck 1 has the rope attached to its center and Puck 2 has the rope wound about its edge (see below).
 {{ 183_notes:hand_puck.png }}
-=== Both pucks travel the same distance ===
+==== Both Pucks Travel The Same Distance ====
 Both pucks start from rest and are pulled with the same force ($F_T$) over the same amount of time. But, Puck 2 will rotate as the rope is unwound from the edge of the puck. Because both pucks experience the same force over the same time, both will have the same final momentum,
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 $$\Delta K_{trans} = \dfrac{1}{2}m\,v_{cm}^2 = W_{cm} = F_T\,d$$
-=== Where does the rotational energy come from? ===
+==== Where does the rotational energy come from? ====
 But why does Puck 2 rotate? You know there's [[183_notes:rot_ke|energy associated with rotation]]. If both pucks experience the same work in the point particle system, why does Puck 2 rotate?
-The point particle system can only describe the translation kinetic energy of a system. For Puck 1, the point particle and real system are exactly the same. Puck 1 only has translational kinetic energy.
+The point particle system can only describe the translation kinetic energy of a system. For Puck 1, the point particle and real system are exactly the same. **Puck 1 only has translational kinetic energy.**
-But Puck 2 has rotational kinetic energy also. So, you must analyze the energy in the real system. For now, let's assume there's only changes in kinetic energy (translation and rotation) and no thermal energy changes (and no Q).
+**But Puck 2 has rotational kinetic energy also.** So, you must analyze the energy in the real system. For now, let's assume there's only changes in kinetic energy (translation and rotation) and no thermal energy changes (and no Q).
 $$\Delta K_{tot} = \Delta K_{trans} + \Delta K_{rot} = W_{surr}$$