Steps for Calculating Torque

Step 1 : Make a tilt of know quantities including the order of magnitude of the force, the magnitude of the pry branch, and the lean between the force and the lever arm vectors .
Step 2 : ersatz these quantities into the equality { equivalent } \tau = |r|\ |F| \sin { \theta } { /eq } to calculate the torsion .
Step 3 : Apply the right hand rule to determine the direction of the torsion .

Formula and Vocabulary for Calculating Torque

Torque : Torque, { equivalent } \tau { /eq }, is the condition given to a wedge that causes an aim to change its angular ( rotational ) speed. This happens when a force is applied to the object at some distance from its detail of rotation.

Lever Arm : The pry weapon, { equivalent } r { /eq }, is a distance vector trace from the degree of an object ‘s rotation to the point of application of the enforce power .
Formula for Torque : The rule for calculating torsion is { equivalent } \tau = |r|\ |F| \sin { \theta } { /eq }, where { eq } |r| { /eq } is the order of magnitude of the lever arm, { equivalent } |F| { /eq } is the magnitude of the pull vector, and { eq } \theta { /eq } is the angle formed between the wedge and pry arm vectors .
Right Hand Rule for Torque : The management of the torsion vector is found using the right hand rule :

1. Starting at the point of rotation, point the fingers of your right hand toward the point of application of the force.
2. Curl your fingers in the direction of the force vector and extend your thumb outward from your hand.
3. Your thumb is pointing in the direction of the torque. Conventionally, if your thumb is pointing out of the page, the torque is positive. If your thumb is pointing into the page, the torque is negative.

The keep up three example problems demonstrate how to calculate torsion .

Example Problem 1 – Calculating Torque

A 1.5-meter long browning automatic rifle is oriented horizontally and pinned so that it rotates about its forget end. A 20-N up force is applied to a orient 0.4 meters from the left side of the browning automatic rifle. What is the torsion applied to the bar ?
Step 1 : We will first make a list of all given quantities. In this case, we have the pry arm magnitude, the effect order of magnitude, and the angle between them ( which is just 90 degrees because the lever arm is pointed to the right and the coerce is pointed up ) :

• {eq}|r| = 0.4\ \rm{m}

  {/eq}

• {eq}|F| = 20\ \rm{N}

  {/eq}

• {eq}\theta = 90 ^\circ

  {/eq}

Notice that the distance of the banish is not needed for any calculation .
Step 2 : We will substitute these values into the torsion equation to solve for the order of magnitude of the torsion :
$ $ \tau = |r|\ |F| \sin { \theta } = ( 0.4\ \rm { m } ) ( 20\ \rm { N } ) \sin { 90 ^\circ } = 8.0\ \rm { N\cdot megabyte } $ $
Step 3 : The direction ( positive or negative ) of the torsion can be found by using the correctly pass rule. In this character, starting signal at the left field side of the bar and point the fingers of your right hand toward the proper ( in the direction of the point of application of the force ). Curl your fingers in the direction of the pull vector. Your flick should be pointing out of the page which is the plus direction .
The torsion in this trouble is { equivalent } \tau = +8.0\ \rm { N\cdot m } { /eq } .

Example Problem 2 – Calculating Torque

A vertically-oriented bar is pinned so that it rotates about its top end. At a degree 0.75 meters below the top pin, a 15-N military unit is applied to the bar to the right at an slant of 20 degrees below the horizontal. What is the torsion acting on the bar ?
Step 1 : First, make a number of all the known quantities. The angles in this one can be a short crafty, so it might be useful to draw a visualize of the position :

Notice that flush though the given slant in the trouble is 20 degrees, the angle between the lever weapon and the effect vectors is actually the complement of this fish. consequently :

• {eq}|r| = 0.75\ \rm{m}

  {/eq}

• {eq}|F| = 15\ \rm{N}

  {/eq}

• {eq}\theta = 90 ^\circ – 20 ^\circ = 70 ^\circ

  {/eq}

Step 2 : We will substitute these into the torsion equality :
$ $ \tau = |r|\ |F| \sin { \theta } = ( 0.75\ \rm { m } ) ( 15\ \rm { N } ) \sin { 70 ^\circ } \approx 11\ \rm { N\cdot molarity } $ $
Step 3 : To find the direction of the torsion, point your fingers downward and curl them to the right. Your flick points out of the page which indicates a convinced torsion .
The torsion on the stripe is { equivalent } \tau = +11\ \rm { N\cdot m } { /eq }

Example Problem 3 – Calculating Torque

A vertically-oriented 0.80-m long measure is pinned so that it rotates about its top goal. A 120-N force is applied directly up at the bottom conclusion of the bar. What is the torsion acting on the bar ?
Step 1 : We will list the given quantities :

• {eq}|r| = 0.80\ \rm{m}

  {/eq}

• {eq}|F| = 120\ \rm{N}

  {/eq}

• {eq}\theta = 180 ^\circ

  {/eq}

The angle is 180 degrees because the pry arm vector points straight polish and the wedge vector points straight up .
Step 2 : We will plug these variables into the torsion equality :
$ $ \tau = |r|\ |F| \sin { \theta } = ( 0.80\ \rm { m } ) ( 120\ \rm { N } ) \sin { 180 ^\circ } = 0 $ $
Since the vectors are latitude, there is no torsion applied to the banish.

Step 3 : Since there is no torsion, there is no direction associated with it .
There is no torsion acting on this measure .

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