Physics 15 Torque Fundamentals (5 of 13) How to Calculate a Torque (Method 2)

Michel van Biezen
2 May 201603:34
EducationalLearning
32 Likes 10 Comments

TLDRThe video script explains an alternative method for calculating torque, which is the force that causes an object to rotate around a pivot point. It describes how to determine the torque by multiplying the force's magnitude by the perpendicular distance from the force's line of action to the pivot point. The script illustrates this with a right triangle, where the perpendicular distance is found by multiplying the object's length (hypotenuse) by the cosine of the angle between the force's direction and the pivot. An example is provided using a force of 20 Newtons, an object length of 4 meters, and a 30-degree angle, resulting in a torque of approximately 69 Newton-meters. The method is emphasized as a valuable approach in certain situations where it simplifies the calculation process.

Takeaways
  • πŸ“ **Torque Calculation Method**: Torque can be calculated by multiplying the force magnitude by the perpendicular distance from the force's line of action to the pivot point.
  • πŸ” **Line of Action**: The line of action is the direction in which the force is applied to the object, and a line drawn from the pivot to this line perpendicularly defines the perpendicular distance.
  • ➑️ **Perpendicular Distance**: The perpendicular distance is the length from the pivot point to the line of action of the force, forming a right triangle with the force's line of action.
  • πŸ“ **Right Triangle Relation**: The perpendicular distance is equal to the hypotenuse (length L of the object) times the cosine of the angle (theta) between the force's line of action and the object.
  • πŸ”’ **Torque Equation**: The torque is equal to the magnitude of the force times the length of the object times the cosine of the angle theta.
  • πŸ“ˆ **Cosine Function**: The cosine function is used to find the perpendicular distance when the angle and the length of the object are known.
  • πŸ“š **Consistency in Equations**: The method presented yields the same torque equation as previous methods, just approached differently.
  • πŸ› οΈ **Practical Application**: This method can be easier in certain situations, depending on the setup of the problem and the diagram provided.
  • πŸ“ **Example Calculation**: Given a length of 4 meters, an angle of 30 degrees, and a force of 20 Newtons, the torque can be calculated as 20 N * 4 m * cos(30Β°), resulting in approximately 69 Newton-meters.
  • πŸ”§ **Situational Advantage**: Sometimes calculating torque using the perpendicular distance can be more straightforward, depending on the specific problem configuration.
  • βœ… **Same Result, Different Approach**: The final result remains the same regardless of the method used to calculate torque, emphasizing the importance of understanding multiple approaches.
Q & A
  • What is the concept of torque in physics?

    -Torque is the measure of the force that can cause an object to rotate about an axis, and it is calculated by multiplying the force's magnitude by the perpendicular distance from the pivot point to the line of action of the force.

  • How is the line of action of a force defined?

    -The line of action of a force is a line in the same direction as the force is acting and is used to determine the point at which the force is applied.

  • What is the perpendicular distance in the context of calculating torque?

    -The perpendicular distance is the shortest distance from the pivot point to the line of action of the force, measured at a right angle to the line of action.

  • How does one find the perpendicular distance to the line of action of the force?

    -The perpendicular distance can be found by drawing a line from the pivot point to the line of action of the force, ensuring it is perpendicular. This forms a right triangle, where the perpendicular distance is the adjacent side, and the hypotenuse is the length of the object (L).

  • What is the relationship between the perpendicular distance and the length of the object?

    -The perpendicular distance is related to the length of the object (L) and the angle (theta) between the force and the object by the equation: perpendicular distance = L * cos(theta).

  • What is the formula for calculating torque using the magnitude of force, the length of the object, and the cosine of the angle?

    -The formula for torque is given by: Torque = Magnitude of force * Length of the object (L) * Cosine of the angle (theta).

  • How does the method of calculating torque by finding the perpendicular distance differ from other methods?

    -This method involves directly calculating the perpendicular distance using geometry and trigonometry, rather than working with the cosine of the angle directly, which can sometimes be more straightforward depending on the setup of the problem.

  • In the example given, what are the values for the length of the object, the angle, and the magnitude of force?

    -In the example, the length of the object is 4 meters, the angle is 30 degrees, and the magnitude of force is 20 Newtons.

  • What is the calculated torque in the example provided, if we round it off?

    -The calculated torque in the example is approximately 69 Newton-meters when rounded off.

  • Why might this method of calculating torque sometimes be easier than others?

    -This method might be easier when the situation or the diagram of the system being analyzed is more conducive to geometric interpretation and when the perpendicular distance can be clearly identified and measured.

  • What is the significance of using different methods to calculate torque?

    -Different methods can offer alternative perspectives and can be more convenient or simpler to apply in certain scenarios, providing flexibility and ensuring accuracy in a variety of situations.

  • How does the cosine function play a role in the calculation of torque?

    -The cosine function is used to relate the angle between the force vector and the lever arm (the perpendicular distance from the pivot to the line of action of the force), allowing for the calculation of torque even when the force is not directly aligned with the lever arm.

Outlines
00:00
πŸ”§ Understanding Torque Calculation with Perpendicular Distance

This paragraph explains an alternative method for calculating torque. It involves an object with a length L that can pivot around one end and a force applied at the other end. Torque is calculated by multiplying the force's magnitude by the perpendicular distance from the force's line of action to the pivot point. The line of action is the direction in which the force is applied, and the perpendicular distance is found by drawing a line from the pivot point to this line of action. The paragraph also explains how to find this distance by creating a right triangle, where the perpendicular distance is equal to the hypotenuse (length L) times the cosine of the angle theta. The torque formula is then derived as the force magnitude times the object's length times the cosine of theta. An example calculation is provided using a force of 20 Newtons, a length of 4 meters, and an angle of 30 degrees, resulting in a torque of approximately 69 Newtons.

Mindmap
Keywords
πŸ’‘Torque
Torque is the rotational force that can cause an object to rotate around an axis. It is a key concept in the video as it is the main subject being explained. The video defines torque as the product of the force applied and the perpendicular distance from the pivot point to the line of action of the force. An example used in the script is calculating the torque when a force of 20 Newtons is applied to an object that is 4 meters long at an angle of 30 degrees.
πŸ’‘Pivot Point
The pivot point is the point around which an object can rotate or turn. In the context of the video, it is the reference point from which the perpendicular distance to the line of action of the force is measured. The pivot point is essential for calculating torque, as it helps determine the effectiveness of the force in causing rotation.
πŸ’‘Line of Action
The line of action refers to the straight path along which a force is applied or acts on an object. It is mentioned in the video to illustrate the direction in which the force is acting and how it relates to the pivot point to calculate torque. The line of action is perpendicular to the pivot point when determining the perpendicular distance.
πŸ’‘Perpendicular Distance
This is the distance measured at a right angle from the pivot point to the line of action of the force. The video emphasizes that this distance is crucial for calculating torque. It is used in the formula for torque, where the force magnitude is multiplied by the perpendicular distance to find the torque value.
πŸ’‘Magnitude of Force
The magnitude of force is the strength or quantity of the force applied to an object. It is a fundamental component in the calculation of torque, as shown in the formula where torque equals the magnitude of force times the perpendicular distance. In the example provided, the magnitude of force is given as 20 Newtons.
πŸ’‘Right Triangle
A right triangle is a geometric figure with one 90-degree angle. The concept is used in the video to explain how to find the perpendicular distance from the line of action to the pivot point. By forming a right triangle, one can use trigonometric functions, such as cosine, to calculate the perpendicular distance.
πŸ’‘Hypotenuse
The hypotenuse is the longest side of a right triangle, opposite the right angle. In the context of the video, the hypotenuse is the length of the object (L), which is used in conjunction with the cosine of the angle to find the perpendicular distance, a necessary step in calculating torque.
πŸ’‘Cosine of the Angle
The cosine of the angle is a trigonometric function that describes the ratio of the adjacent side to the hypotenuse in a right triangle. In the video, it is used to relate the length of the object (hypotenuse) to the perpendicular distance, which is essential for calculating torque. The cosine function is applied to the angle ΞΈ in the formula for torque.
πŸ’‘Newtons
Newtons are the unit of measurement for force in the International System of Units (SI). The video uses Newtons to quantify the magnitude of the force applied to the object. Understanding Newtons is important for grasping how force magnitude contributes to the calculation of torque.
πŸ’‘Length of the Object
The length of the object (L) is the distance from where the force is applied to the pivot point. It is a key parameter in the torque calculation, as it is part of the formula that multiplies the force's magnitude by the length and the cosine of the angle to yield the torque.
πŸ’‘Angle Theta
Angle Theta (ΞΈ) is the angle formed between the line of action of the force and the perpendicular line drawn from the pivot point. The video explains that the cosine of this angle is used to find the perpendicular distance, which is then used to calculate the torque. The angle is a crucial factor in determining the effectiveness of the force in producing torque.
Highlights

Introduction to a different method for calculating torque.

Torque is calculated by multiplying the force's magnitude by the perpendicular distance from the force's line of action to the pivot point.

Demonstration of drawing the line of action of the force.

Explanation of the perpendicular distance as the distance from the force's line of action to the pivot point.

Formation of a right triangle to find the perpendicular distance.

The perpendicular distance is equal to the hypotenuse times the cosine of the angle theta.

Torque formula involving the magnitude of force, object length, and cosine of theta.

Comparison of this method to previous methods, emphasizing its practicality in certain situations.

Example calculation using the new method with given values: length (4m), angle (30 degrees), and force (20 Newtons).

Calculation result of torque using the example values, yielding 69 Newtons.

Emphasis on the method's utility despite its complexity in certain scenarios.

Highlighting the value of approaching torque calculation in this manner for specific setups.

Explanation of how the cosine of theta is integrated into the calculation without directly working with the angle.

Illustration of the process to find the torque by drawing the line from the pivot point to the line of action.

Clarification that the method simplifies to the same torque equation as previous methods.

Advantage of this method in situations where the setup makes it more straightforward to find the perpendicular distance.

Use of a calculator to perform the example calculation, emphasizing the practical application of the method.

Final summary of the method's effectiveness and its place in the context of torque calculation.

Transcripts
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