PHYS 121 - Week 6 Lecture 3 - Torque

Summary

This lecture dives into the concepts of angular motion, focusing on torque and the factors that affect rotational acceleration. It discusses how force, distance from the pivot, and the angle of application all influence the ability of a force to rotate an object. Practical examples with a door and a wrench illustrate these principles, including the use of perpendicular force components. The lecture also introduces the right-hand rule for determining the direction of torque and emphasizes the importance of understanding these fundamentals before moving on to more advanced concepts in rotational dynamics.

Takeaways

• 😀 Force causes linear acceleration, but torque causes angular acceleration (rotational motion).
• 😀 Torque depends on three main factors: the magnitude of force, the distance from the axis of rotation, and the angle at which the force is applied.
• 😀 The more distance between the point of force application and the axis of rotation, the more torque is generated.
• 😀 The angle at which force is applied affects the torque: a 90° angle (perpendicular) generates the maximum torque.
• 😀 If a force is applied directly along the axis of rotation, it generates no torque.
• 😀 Torque is a vector, meaning it has both magnitude and direction.
• 😀 The equation for torque is τ = R × F × sin(θ), where R is the distance, F is the force, and θ is the angle between the force and the radial line.
• 😀 In cases where the angle isn’t given, you can use the perpendicular component of either the force or the radius to calculate torque.
• 😀 To calculate torque, the perpendicular component of the force is the only part that contributes to the rotational effect.
• 😀 The right-hand rule is used to determine the direction of the torque vector: point your fingers in the direction of the radius, curl toward the force, and your thumb points in the direction of torque.

Q & A

What is torque, and how is it related to rotational motion?

Torque is a force that causes an object to rotate around an axis or pivot point. It is the rotational counterpart to linear force and is responsible for angular acceleration, just as force causes linear acceleration.

What factors affect the magnitude of torque?

Three factors affect the magnitude of torque: the magnitude of the applied force, the distance from the pivot point (radius), and the angle at which the force is applied relative to the radius. The farther the force is applied from the pivot, the greater the torque.

How does the angle of force application influence torque?

The torque is maximized when the force is applied at a 90-degree angle to the radius. If the force is applied at a smaller or larger angle, only the perpendicular component of the force contributes to the torque, reducing its effectiveness.

What is the formula for calculating torque?

The formula for torque is T = r * F * sin(θ), where T is the torque, r is the distance from the pivot, F is the magnitude of the applied force, and θ is the angle between the force and the radial line from the pivot.

What is the significance of the perpendicular component of the force in torque calculation?

Only the perpendicular component of the applied force contributes to torque. The parallel component, which acts along the radial line, does not generate any torque because it does not induce rotational motion.

In the example with the wrench, how do we calculate the torque exerted by Lewis?

In the wrench example, the torque is calculated by multiplying the perpendicular component of either the force or the radius by the other. In this case, Lewis applies a force of 100 N at a 30-degree angle, and the torque is calculated as T = r * F * cos(30°), resulting in a torque of approximately 17 N·m.

What does it mean for torque to be a vector?

Torque is a vector because it has both magnitude and direction. The direction of the torque vector determines the axis around which the object will rotate, and this direction is determined using the right-hand rule.

How do we use the right-hand rule to determine the direction of the torque vector?

To use the right-hand rule, point your fingers in the direction of the radius (the line from the pivot point), curl them in the direction of the applied force, and your thumb will point in the direction of the torque vector, indicating the direction of rotation.

Why does the distance from the pivot affect torque?

The distance from the pivot affects torque because the farther the force is applied from the pivot point, the larger the lever arm. A larger lever arm means that the force is more effective at causing rotational motion, thus increasing the torque.

What happens if the force is applied at the pivot point or along the radial line?

If the force is applied directly at the pivot point or along the radial line, the torque will be zero. This is because the distance from the pivot is zero or the force is not acting perpendicular to the radius, so no rotational effect is generated.