Physics 15 Torque Fundamentals (11 of 13) How to Calculate the Net Torque? Ex. 2

Michel van Biezen
9 Jun 201603:58
EducationalLearning
32 Likes 10 Comments

TLDRThe video script discusses the concept of net torque on a beam subjected to two forces (F1 and F2) at angles to the perpendicular. It explains that while the principle of torque calculation remains the same, the angles of the forces must be considered. The net torque is calculated by summing the torques from both forces, taking into account their directions to determine if they are positive or negative. The example provided involves calculating the net torque with F1 causing a positive torque and F2 a negative one. The calculation involves multiplying each force by the distance from the pivot and the cosine of the respective angles (θ1 and θ2). The final result is a negative torque, indicating a clockwise rotation. The script emphasizes the importance of considering the direction of the torque when calculating the net torque.

Takeaways
  • 📐 **Angle Consideration**: Unlike the previous example, both forces (F1 and F2) are now acting at an angle relative to the perpendicular of the beam, which must be taken into account when calculating torque.
  • ⚙️ **Net Torque Calculation**: The net torque is the sum of the torques caused by each force (torque1 + torque2), considering their directions and whether they contribute positively or negatively to the rotation.
  • ➕ **Positive Torque by F1**: Force F1, if acting alone, would cause a counterclockwise rotation, which is considered a positive torque.
  • ➖ **Negative Torque by F2**: Force F2, if acting alone, would cause a clockwise rotation, resulting in a negative torque.
  • 🔢 **Torque Formula**: The torque caused by a force is calculated as the product of the force, the distance from the pivot to where the force is applied, and the cosine of the angle between the force's direction and the perpendicular.
  • 📐 **Cosine of Angles**: The cosine of the angle (θ1 for F1 and θ2 for F2) is used to determine the component of the force that contributes to the torque.
  • 🔢 **Force and Distance**: The force values (40 Newtons for F1 and 30 Newtons for F2) and the distance from the pivot point (half the length of the beam, L/2) are used in the torque calculation.
  • 📐 **Cosine Values**: Cosine of 20 degrees (θ1) is approximately 0.94, and cosine of 30 degrees (θ2) is 0.866, which are used to find the torque values for each force.
  • 🔢 **Calculation Example**: For F1, the torque is calculated as 40 Newtons times 2 meters (half the beam's length) times cosine of 20 degrees. For F2, it's 30 Newtons times the full length of the beam (2 meters) times cosine of 30 degrees.
  • 🔢 **Net Torque Result**: The net torque is found by subtracting the torque caused by F2 from that caused by F1, resulting in a negative value indicating a clockwise torque.
  • ➡️ **Direction of Torque**: A negative torque value signifies a clockwise direction of the torque, which in this context means the beam will rotate into the board.
  • 📝 **Final Consideration**: It's important to consider the direction of the torque when interpreting the results, as it affects the understanding of how the forces will rotate the beam.
Q & A

  • What is the primary concept being discussed in the transcript?

    -The primary concept discussed is the calculation of net torque on a beam when forces are acting at an angle relative to the perpendicular of the beam.

  • How does the direction of force affect the torque on the beam?

    -The direction of the force affects the torque by determining whether the torque is positive (counterclockwise rotation) or negative (clockwise rotation).

  • What is the formula for calculating the net torque when forces are acting at an angle?

    -The net torque is calculated as the sum of the individual torques, taking into account the cosine of the angle between the force's direction and the perpendicular.

  • What is the significance of cosine in the torque calculation?

    -The cosine function is used to adjust the force's value based on the angle it makes with the perpendicular to account for the effective force component that contributes to the torque.

  • What does a negative torque value indicate in the context of the beam?

    -A negative torque value indicates that the combined effect of the forces will cause a clockwise rotation of the beam.

  • How is the direction of the torque related to the net torque's sign?

    -The sign of the net torque corresponds to the direction of the intended rotation: positive for counterclockwise and negative for clockwise.

  • What are the two forces, F1 and F2, acting on the beam in the example?

    -In the example, F1 is 40 Newtons and F2 is 30 Newtons, both acting at different angles to the perpendicular of the beam.

  • What is the length of the beam in the given example?

    -The length of the beam in the example is 2 meters.

  • What are the angles, theta1 and theta2, associated with the forces F1 and F2 respectively?

    -Theta1 is 20 degrees associated with force F1, and theta2 is 30 degrees associated with force F2.

  • How does one determine the effective torque caused by each force?

    -The effective torque for each force is determined by multiplying the force by the perpendicular distance from the pivot point to where the force is acting, and then by the cosine of the angle the force makes with the perpendicular.

  • What is the final calculated net torque on the beam in the example?

    -The final calculated net torque is -14.4 Newton meters, indicating a clockwise torque.

  • Why is it important to consider the angle of the forces when calculating torque?

    -Considering the angle is important because it determines the effective component of the force that produces torque, which is crucial for accurately calculating the potential rotation or twisting effect on the beam.

Outlines
00:00
📐 Calculating Net Torque with Angled Forces

This paragraph discusses the calculation of net torque on a beam subjected to two forces, F1 and F2, which are not perpendicular to the beam but act at an angle. The principle of torque calculation remains the same, but the angles of the forces must be considered. The net torque is the sum of the individual torques, taking into account their directions to determine if they are positive or negative. F1 causes a positive torque as it would rotate the beam counterclockwise, while F2 causes a negative torque as it would rotate the beam clockwise. The net torque is calculated by multiplying each force by its respective distance from the pivot point (L/2 for F1 and L for F2) and the cosine of the angle between the force's direction and the perpendicular (θ1 for F1 and θ2 for F2). Substituting the given values (F1 = 40 N, F2 = 30 N, L = 2 m, θ1 = 20°, θ2 = 30°), we find that the net torque is negative, indicating a clockwise rotation.

Mindmap
Keywords
💡Electron Line
The term 'Electron Line' seems to refer to the subject or the context of the video, which is likely about physics or engineering, specifically dealing with forces and their effects on a beam. It is not explicitly defined in the script but serves as the backdrop for the discussion of forces and torque.
💡Torque
Torque is the rotational equivalent of linear force. It is a measure of the force that can cause an object to rotate around an axis. In the video, torque is central to understanding how forces acting at an angle to a beam result in rotation. The script discusses calculating the net torque as the sum of individual torques caused by forces F1 and F2.
💡Beam
A beam is a structural element that is capable of withstanding load primarily by resisting bending. In the context of the video, the beam is the object upon which forces F1 and F2 are acting, causing it to rotate. The beam's length and the point of application of the forces are critical in calculating torque.
💡Forces F1 and F2
F1 and F2 are the two forces being considered in the video. They act on the beam at different angles to the perpendicular, which is a departure from the previous example where forces acted perpendicularly. The magnitudes of these forces (40 Newtons for F1 and 30 Newtons for F2) and their angles of application (20 degrees for F1 and 30 degrees for F2) are used to calculate the net torque.
💡Angles
The angles are critical in determining the direction and magnitude of the torque. They are the angles between the forces F1 and F2 and the perpendicular to the beam. The cosine of these angles (theta sub 1 and theta sub 2) is used in the torque calculations, indicating the direction of the force's effect in relation to the beam's rotation.
💡Cosine
The cosine function is used in trigonometry to find the adjacent side of a right-angled triangle from the angle. In the video, cosines of the angles (theta sub 1 and theta sub 2) are used to adjust the force magnitudes according to the direction of the forces relative to the perpendicular, thus affecting the calculation of torque.
💡Net Torque
Net torque is the total torque acting on an object, resulting from the vector sum of all the individual torques. In the video, the net torque is calculated by adding the torques caused by F1 and F2. It determines the overall effect of the forces on the rotation of the beam.
💡Positive and Negative Torque
Positive and negative torque indicate the direction of rotation caused by the forces. A positive torque, as caused by F1, would result in counterclockwise rotation, while a negative torque, such as that caused by F2, would result in clockwise rotation. The net torque's sign indicates the overall direction of the beam's rotation.
💡Clockwise and Counterclockwise
These terms describe the direction of rotation. In the context of the video, they are used to describe the effect of the forces on the beam's rotation. Clockwise rotation is associated with negative torque, while counterclockwise rotation is associated with positive torque.
💡Pivot Point
The pivot point is the point around which an object rotates. In the video, it is the reference point from which the distances to the forces acting on the beam are measured. The pivot point is crucial for determining the leverage and thus the torque produced by the forces.
💡Newton Meters
Newton meters is a unit of measurement for torque. It is derived from the basic units of force (Newtons) and distance (meters). In the video, the calculation of torque is expressed in Newton meters, indicating the product of the force applied and the distance from the pivot point.
Highlights

The example demonstrates the calculation of net torque on a beam with forces acting at an angle to the perpendicular.

Both forces F1 and F2 are no longer perpendicular to the length of the beam, introducing an angle into the torque calculation.

Torque is calculated as the sum of torques from individual forces, considering their directions.

Force F1 causes a positive torque, indicating a counterclockwise rotation.

Force F2 results in a negative torque, implying a clockwise rotation.

Net torque is calculated by summing the individual torques, taking into account their positive or negative values.

The formula for net torque includes the cosine of the angle between the force's direction and the perpendicular.

The distance from the pivot point to where the force is acting is factored into the torque calculation.

The net torque is the difference between the torque caused by F1 (positive) and F2 (negative).

Force F1 is 40 Newtons, and Force F2 is 30 Newtons, with the beam length being 2 meters.

Cosine of the angles (theta1 and theta2) are used to determine the direction and magnitude of the torques.

The cosine of 20 degrees is approximately 0.94, used for F1's torque calculation.

The cosine of 30 degrees is used for F2's torque calculation, resulting in a negative value.

The net torque is calculated to be negative, indicating a clockwise rotation.

The negative sign of the net torque indicates the direction of the torque is clockwise.

The practical application is understanding how forces at an angle affect the rotational dynamics of a beam.

The example concludes by emphasizing the importance of considering the direction of torque in calculations.

Transcripts

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Engineering PrinciplesTorque AnalysisBeam MechanicsForce AnglesNet TorqueCounterclockwiseClockwise RotationCosine FunctionNewton's LawsMechanical EngineeringPhysics ConceptsEngineering Calculation