183_notes:torque

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183_notes:torque [2018/05/30 18:20] – hallstein183_notes:torque [2021/05/08 18:55] – [Torque] stumptyl
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 ===== Torques Cause Changes in Rotation ===== ===== Torques Cause Changes in Rotation =====
  
-Until now, you have worked with [[183_notes:mp_multi|forces]] and [[183_notes:work|work]] to explain and predict the motion of objects. You've even used [[183_notes:rot_ke|work and energy to begin to explain that objects can rotate]], but you haven't yet unpacked how that occurs -- only that a system can share energy between translation and rotation. In these notes, you will read about torque, which is a force applied at a distance from a specific point that causes a twisting or rotating about that point.+Until now, you have worked with [[183_notes:mp_multi|forces]] and [[183_notes:work|work]] to explain and predict the motion of objects. You've even used [[183_notes:rot_ke|work and energy to begin to explain that objects can rotate]], but you haven't yet unpacked how that occurs -- only that a system can share energy between translation and rotation. **In these notes, you will read about torque, which is a force applied at a distance from a specific point that causes a twisting or rotating about that point.**
 ==== Lecture Video ==== ==== Lecture Video ====
  
 {{youtube>SrRoXGqRNi8?large}} {{youtube>SrRoXGqRNi8?large}}
  
-==== Torque ====+===== Torque =====
  
 {{ 183_notes:torque_and_ang_momentum.001.png?300}} {{ 183_notes:torque_and_ang_momentum.001.png?300}}
  
-//Torque is a vector quantity that describes how you can change the rotation of an object.// Specifically, the torque about a point A is the vector (cross) product of the vector that points from A to the point where the force is applied and the force itself. That's a mouthful, but you can think about it in terms of the figure to the right.+**Torque is a vector quantity that describes how you can change the rotation of an object.**. Specifically, the torque about a point A is the vector (cross) product of the vector that points from A to the point where the force is applied and the force itself. That's a mouthful, but you can think about it in terms of the figure to the right.
  
 Consider a bolt that is located at A in the figure to the right. You attach a wrench to location A and push on the end of the wrench with the force indicated. The vector that points from A to the end of the wrench where the force is applied is $\vec{r}_A$. This distance is often called the "lever arm." It indicates the point of application of the force relative to the rotation axis.  Consider a bolt that is located at A in the figure to the right. You attach a wrench to location A and push on the end of the wrench with the force indicated. The vector that points from A to the end of the wrench where the force is applied is $\vec{r}_A$. This distance is often called the "lever arm." It indicates the point of application of the force relative to the rotation axis. 
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 $$\vec{\tau}_{A} = \vec{r}_A \times \vec{F}$$ $$\vec{\tau}_{A} = \vec{r}_A \times \vec{F}$$
  
-The //torque is a vector//; it has both a magnitude and direction. The units of torque are Newton-meters ($\mathrm{Nm}$). This is the first physical quantity that you have seen that seen that depends on the cross (vector) product between two vectors. It's worth taking some time to understand how this mathematics works.+The **torque is a vector**; it has both a magnitude and direction.** The units of torque are Newton-meters ($\mathrm{Nm}$)**. This is the first physical quantity that you have seen that depends on the cross (vector) product between two vectors. It's worth taking some time to understand how this mathematics works.
  
-=== The magnitude of the torque ===+==== The Magnitude of the Torque ====
  
-The magnitude of the the torque depends on the component of the force that is perpendicular to the lever arm. In the figure above, the perpendicular component of the force is given by,+**The magnitude of the torque depends on the component of the force that is perpendicular to the lever arm**. In the figure above, the perpendicular component of the force is given by,
  
 $$F_{\perp} = F\sin\theta$$ $$F_{\perp} = F\sin\theta$$
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 So, as shown in the figure to the right, the torque is only due to the component of the force that is perpendicular to the lever arm ($F_{\perp}$). So, as shown in the figure to the right, the torque is only due to the component of the force that is perpendicular to the lever arm ($F_{\perp}$).
  
-=== The direction of the torque ===+==== The Direction of the Torque ====
  
 Torque is a vector quantity; it has a direction. How can you determine that direction?  Torque is a vector quantity; it has a direction. How can you determine that direction? 
  • 183_notes/torque.txt
  • Last modified: 2021/05/08 18:56
  • by stumptyl