37239 Lecture : Torque notes

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kpatil

4 Mar 2023

School

UC-Davis

Department

Physics

Course

PHY9A

Professor

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Document Summary

Torque is a measure of the force that causes an object to rotate around an axis or pivot point. It is an important concept in physics and engineering, particularly in the design and operation of machines and mechanisms. One way to determine torque is by using principles of geometry. Specifically, torque can be calculated as the product of force and the perpendicular distance from the axis of rotation to the point where the force is applied. Torque = force x perpendicular distance where torque is measured in units of newton-meters (nm), force is measured in units of newtons (n), and perpendicular distance is measured in units of meters (m). To illustrate this concept, consider the following example. Suppose a person is using a wrench to turn a bolt. The person applies a force of 50 n to the end of the wrench, which is 0. 3 meters away from the center of the bolt.

Related Questions

The tangential force method involves finding the component of the applied force that is perpendicular to the displacement from the pivot point to where the force is applied. This perpendicular component of the force is called the tangential force.

(a) What is , the magnitude of the tangential force that acts on the pole due to the tension in the rope?

Express your answer in terms of

and

.

When using the tangential force method, you calculate the torque using the equation

$\tau = f_{\rm t} d$ ,

where

is the distance from the pivot to the point where the force is applied. The sign of the torque can be determined by checking which direction the tangential force would tend to cause the pole to rotate (where counterclockwise rotation implies positive torque).

(b) What is the magnitude of the torque

on the pole, about point A, due to the tension in the rope?

Express your answer in terms of

, and

The moment arm method involves finding the effective moment arm of the force. To do this, imagine a line parallel to the force, running through the point at which the force is applied, and extending off to infinity in either direction. You may shift the force vector anywhere you like along this line without changing the torque, provided you do not change the direction of the force vector as you shift it. It is generally most convenient to shift the force vector to a point where the displacement from it to the desired pivot point is perpendicular to its direction. This displacement is called the moment arm.

For example, consider the force due to tension acting on the pole. Shift the force vector to the left, so that it acts at a point directly above point A in the figure. The moment arm of the force is the distance between the pivot and the tail of the shifted force vector. The magnitude of the torque about the pivot is the product of the moment arm and force, and the sign of the torque is again determined by the sense of the rotation of the pole it would cause.

, the length of the moment arm of the force.

Express your answer in terms of

and

(d)Now consider a woman standing on the ball of her foot as shown. A normal force of magnitude

acts upward on the ball of her foot. Achilles' tendon is attached to the back of the foot. The tendon pulls on the small bone in the rear of the foot with a force

. This small bone has a length

, and the angle between this bone and the Achilles' tendon is

. The horizontal displacement between the ball of the foot and the point P is

Find τp, the torque about point P due to the force applied by the Achilles' tendon. Express your answer in terms of F, ϕ, and x.

turquoiseworm20

The perpendicular distance between the line of force and the axis defines what?

Torque can be calculated by multiplying the force (N) applied at 90^∘to the lever arm at a distance (m) from the pivot point (point of rotation), the compound SI unit for the torque is N⋅m. If the force (at 90^∘ to the lever arm) applied is 15 N and it is applied at 2.0 m from the pivot point (point of rotation), what is the torque on the lever?

Express the torque with the appropriate units.

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37239 Lecture : Torque notes

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