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Explain How is torque calculated using a moment arm?

Short Answer

Expert verified
Torque is calculated as the product of force and moment arm, \( \tau = F \times r \).

Step by step solution

01

Understanding Torque

Torque is a measure of the rotational force applied to an object around a pivot point or axis. It determines how effectively a force can cause an object to rotate.
02

Identifying Components

To calculate torque, we need two key components: the force applied and the moment arm (the perpendicular distance from the axis of rotation to the line of action of the force).
03

Torque Formula

The formula for calculating torque is given by \( \tau = F \times r \) where \(\tau\) is the torque, \(F\) is the force applied, and \(r\) is the moment arm.
04

Applying the Right Angle

The force must be perpendicular to the moment arm to calculate torque effectively. If the force is at an angle, use the perpendicular component of the force.
05

Calculating Torque

Substitute the values from the problem into the torque formula. Multiply the magnitude of the force by the moment arm to find the torque. Ensure correct units are used for both components.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Moment Arm
When discussing how objects rotate, understanding the moment arm is crucial. The moment arm is a pivotal concept in the calculation of torque. It refers to the perpendicular distance from the axis of rotation to the line of action of the force.
This is the "arm" through which the force acts to create rotational movement.
To visualize this, think about a wrench turning a bolt.
The moment arm would be the length of the wrench from the bolt (the axis of rotation) to where your hand applies force.
Using a longer wrench means a longer moment arm, which makes it easier to turn the bolt with the same amount of force applied.
  • The moment arm can affect the ease of rotation.
  • A longer moment arm requires less force to achieve the same rotational effect.
  • Always measure the moment arm perpendicular to the line of force to ensure accuracy in calculations.
Rotational Force
Rotational force, often referred to as torque, is the twisting force that causes an object to rotate around an axis.
It is essentially a measure of how effectively a force can cause an object to spin or twist.
Torque is not just about the amount of force applied, but also where and how that force is applied.
This is because the effectiveness of force in causing rotation depends largely on its distance from the pivot point.
To enhance your understanding of rotational force, consider these points:
  • Torque is maximized when the force is applied perpendicular to the moment arm.
  • If the force is applied directly at the axis of rotation, it won't cause rotation, no matter the magnitude.
  • The units of torque are typically Newton-meters (Nm) or pound-feet (lb-ft).
Taking these into account will help in applying the concept of torque correctly in practical scenarios.
Axis of Rotation
In physics, the axis of rotation is the straight line around which an object rotates or spins.
This is the pivotal point that defines how the object turns.
Understanding the axis of rotation is essential for accurately calculating torque.
Consider a seesaw: the axis of rotation is the pivot point in the middle.
When one side is pushed down, the axis remains stationary as the seesaw rotates around it.
Here are some key points about the axis of rotation:
  • It remains fixed as the object rotates around it.
  • Identifying the correct axis of rotation is vital for torque calculations.
  • The effectiveness of a force in causing rotation varies with the distance from this axis.
By understanding the axis of rotation, one can better understand how different forces affect an object's rotation, leading to more accurate engineering and physics calculations.

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Most popular questions from this chapter

A rigid object rotates about a fixed axis. Do all points on the object have the same angular speed? Do all points on the object have the same linear speed? Explain.

How much time does it take for a spinning baseball with an angular speed of \(38 \mathrm{rad} / \mathrm{s}\) to rotate through \(15^{\circ}\) ?

Dragonflies often dip into the water on the surface of a lake or pond, presumably to drink or to clean themselves. Recently, it has been discovered that after dipping the dragonflies fly straight upward, then pitch forward and tumble head over tail several times until the water has been shed from their bodies. Observations show that the dragonflies complete one revolution every \(0.017 \mathrm{~s}\) during this "spin dry" maneuver. What is their angular speed in radians per second and revolutions per minute? (For comparison, a typical car engine runs at about \(1500 \mathrm{rpm}\).)

Two students sit on either side of a teeter-totter that is \(2.8 \mathrm{~m}\) in length. The teeter-totter balances when the student on the left side is \(1.1 \mathrm{~m}\) from the center and the student on the right is \(1.4 \mathrm{~m}\) from the center. The total mass of the two students is \(84 \mathrm{~kg}\). What is the mass of the student on the left side of the teeter- totter? (Assume that the teeter-totter itself pivots at the center and produces zero torque.)

The Crab Nebula One of the most studied objects in the night sky is the Crab Nebula. It is the remains of a supernova explosion observed by the Chinese in 1054. In 1968 it was discovered that a pulsar-a rapidly rotating neutron star that emits a pulse of radio waves with each revolution-lies near the center of the Crab Nebula. The amount of time required for each rotation of this pulsar is \(33 \mathrm{~ms}\). What is the angular speed (in \(\mathrm{rad} / \mathrm{s}\) ) of the pulsar?

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