Muscle Torque

"Show Me Your Muscles"

Muscle Torque Muscle Torque

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Table of contents

    Man showing his muscles, image by Pixabay CC0 Public Domain StudySmarterA man showing his biscep muscle, which is used to flex the arm and forearm image by Pixabay CC0 Public Domain

    Did you know that we have over 600 muscles in our bodies? Muscles are all made up of the same material, a type of elastic tissue (sort of like the material in a rubber band). Thousands, or even tens of thousands, of small fibers, make up each muscle. You have three different types of muscles in your body: smooth, cardiac, and skeletal. For this article, we will focus on skeletal muscle.

    You've probably heard someone say "Show me your muscles", right? Well, this is a figure of speech and it is not to be taken literally. When someone says " show me your muscles, they aren't asking to look inside your body so your muscles can be seen. What they mean is to say "show me how strong you are" in this particular topic, or "show me how well you can do at this".

    Skeletal muscles are used when we exercise, and they are completely voluntary which means you can control what they do. In Physics, we study the interactions between physical systems. Muscles are no different, we should think of them as part of the physical system of the human body. The movement made by muscles use force or muscular power.

    Muscular power is the power applied when using parts of the body like arms or legs. It is a force that results because of the action of muscles and is a contact force since there is contact between the surfaces. Muscular force is required whenever movement of the body occurs. Strolling, lifting, getting up from a seat, crossing a leg, and so on all require muscular force. Now, let's take a look at how using your muscles relates to simple machines.

    Muscles are a Simple Machine

    Muscles are examples of simple machines.

    Simple machines are devices with no, or very few, moving parts that make work easier.

    In physics, simple machines are devices with no, or very few, moving parts that make work easier. Simple machines are devices that can be used to multiply or augment an applied force. A machine is meant to simply transmit mechanical work from one part of a device to another part. A machine produces force. It controls the direction and the motion of force, but it cannot create energy. A machine's ability to do work is measured by two factors. These two factors are (1) mechanical advantage and (2) efficiency. There are six types of simple machines: the wheel and axle, pulley, lever, wedge, inclined plane, and screw. Muscles are examples of levers.

    A lever is a simple system consisting of a bar, used to provide a force at one end to lift or move a load when a force is placed at the other.

    With a lever, you can either increase the force of the movement, its speed, or its range of motion; but you can’t do all three at the same time. Levers are about tradeoffs; you trade one benefit for another. A lever is composed of a fulcrum, effort, and load.

    1. Fulcrum: the point at which the lever rests and pivots.
    2. Effort (input force): characterized by the amount of work the operator does and is calculated as the force used multiplied by the distance over which the force is used.
    3. Load (output force): the object being moved or lifted; sometimes referred to as resistance.

    There are three classes of levers: First, Second, and Third. There are very few first and second-class levers in the human body.

    The skull as it sits atop the first vertebra allowing the skull to nod forward and backward and side to side is an example of a first-class lever.

    The muscles used when you stand on the tips of your toes would be an example of a second-class lever.

    The elbow joint is an example of third-class lever.

    Muscles Three lever classes StudySmarter OriginalsThree lever classes StudySmarter Originals

    All skeletal muscles provide stability and produce movement in the human body by acting as the force or effort applied to the levers of our bones, and by using opposing forces to achieve a mechanical advantage. To put it another way, muscles move bones around joints.

    Muscle Torque Definition

    Torque: the turning or twisting effectiveness of a force.

    To understand how torque relates to muscles, let's take a look at torque in the general sense. Torque is a measure of how much a force acting on an object causes that object to rotate. The equation for torque is:

    $$T=rf\sin\phi$$

    where \(t\) is the torque, \(r\) is the radius, \(f\) is the force and \(\phi\) is the angle between the force and the arm.

    Muscles create the torques that turn our limbs. When a muscle contracts it pulls on its point of attachment, along the line of action.

    Muscle torque is the force applied by the muscles through a moment arm of a given length, at a given angle to the joint.

    Muscles Woman doing bicep curl with 1kg dumbbell picturing effort, load, and fulcrum, adapted from image by Ivan Radic and flickr, CC by 2.0 StudySmarterClose-up of woman with curly hair doing bicep curl with 1kg dumbbell picturing effort, load, and fulcrum, adapted from image by Ivan Radic and flickr, CC by 2.0

    Forces and Torques in Muscles and Joints

    Muscle torque is the force applied by the muscles through a moment arm. In order to have muscle torque, the joint is needed. The joint, when at different angles will produce variations of muscle torque. Since our muscles can only contract, they occur in pairs throughout our body. In the arm, the bicep muscle is a flexor— that is, it closes the limb. The tricep muscle is an extensor that opens the limb. This configuration is typical of skeletal muscles, bones, and joints in humans. The reason most skeletal muscles exert larger forces than limbs is that most of our muscles are attached to bones via tendons near joints, causing these systems to have mechanical advantages.

    A moment arm is the length between a joint axis and the point where the line of force acts on that joint.

    Muscular Torques

    Torque is crucial for human movement because it is what creates movement at our joints. The moment arm is crucial and some key things to remember about the moment arm are:

    • As the forearm is flexed and extended, the moment arm changes.
    • The moment arm is largest when the elbow is at 90 degrees and gets smaller as it is flexed and extended away from this position(a similar situation exists for most muscles and joints they cross).
    • It explains why muscles are stronger in some joint positions than in others

    To go deeper into how torque and movement in the body relate to everyday motion, let's take a look at some examples of torque in the human body.

    Examples of Torque in the Human Body

    We are probably more aware of external forces on the body happening in everyday life like when we bump into objects. We are not usually aware of internal forces inside the body like muscular forces that cause our blood to circulate. Let's take a look at some examples of torque in the human body.

    Walking:

    • While walking, the torque created at the hip joint help to turn the leg.

    Rotating the hand:

    • The torque acting at the shoulder rotates the hand about the shoulder.

    Turning the head:

    • When we rotate our head around looking from side to side, up or down, muscles in our neck create torque.

    Now that we know torque creates movement at our joints, let's take a closer look at the angle of movement of our muscles.

    Angle of Pull for Muscles

    When we move our muscles, there is an angle of pull that creates force or tension in our movements. This is called "angle of pull".

    Angle of pull is the angle between muscle insertion and bone.

    The angle of pull is the angle between the line of pull and the muscle and bone on which it inserts (angle toward the joint). It is the angle formed between the line of pull of a muscle and the longitudinal axis of the bone in which the muscle is acting.

    It is important to remember these key factors:

    • When there is any degree of motion in the joint, the angle of pull changes.
    • The joint movements and insertion angles involve mostly small angles of pull.
    • The line of pull is usually indicated by the joint angle.
    • The angle of pull affects the strength of muscle action; at only certain angles of pull can a muscle exert maximal tension.
    • Variable resistance exercise machines compensate for variations in muscular tension at different joint angles.

    Muscles The angle of pull of a bicep at the joint showing stabilizing and rotary force components StudySmarter OriginalsThe angle of pull of a bicep at the joint showing stabilizing and rotary force components StudySmarter Originals

    Since the muscle angle of pull determines the type of movement at the joint, by learning where the muscle originates and inserts, you can determine the angle of pull and determine the action of the muscle.

    There are 3 main components of force to the angle of pull:

    • Rotary component: a force of a muscle contributing to bone's movement around a joint axis; greatest when muscles angle of pull is perpendicular to bone (ie: 90 degrees).
    • Stabilizing component: a degree of parallel forces generated on the lever (bone and joint) when the muscle's angle of pull is less than 90 degrees.
    • Dislocating component: a degree of parallel forces generated on the lever (bone and joint) when the muscle's angle of pull is greater than 90 degrees.

    Peak torque is the single highest torque output of the joint produced by muscular contraction.

    If you want to produce the peak torque from a muscle, the joint must be positioned so that the muscle being worked has a 90° angle of pull on the extremity.

    Now, let's try a problem where we calculate muscle torque.

    Muscle torque equation

    We can use this equation for the torque on a muscle when the forces are perpendicular to the moment arm:

    $$T=M_{\text{Arm}}f$$

    Torque = Force multiplied by moment arm

    Step 1:

    Before you sum up the torques, you must identify the forces that have a moment arm and can create a torque.

    To do this, go through the problem, identify each force, and give it a label to stay on track with the equation.

    For this problem, let's say:

    • The weight of the dumbbell can be labeled WD (where D stands for dumbbell).

    • The weight of the forearm/hand segment can be labeled WS (where S stands for segment).

    • The muscle force can be labeled FM (where M stands for muscle).

    Weight is a force that always acts downward. Use a plus sign (+) for the upward direction, and a minus sign (–) for the downward direction. Weights are applied at the center of gravity of a body, and the location of the center of gravity for both the segment and the dumbbell weight are given.

    Step 2:

    Create a table listing what you'll use to calculate the torques, and fill in the known information from the word problem, sort of like this:

    Muscles Torque table for example problem StudySmarter OriginalsTorque table for example problem StudySmarter Originals

    Tips:

    Remember to list weights as negative forces, and the moment arm for each force is on the same side of the elbow joint axis, so set them all as positive.

    The moment arms for the segment weight and the dumbbell weight are the distance of each center of gravity from the elbow axis because the forearm/hand is in a horizontal position.

    The torque created by each force is calculated as a product of the force and moment arm.

    The weights (segment and dumbbell) create negative torques, so it's important to list the direction, and magnitude of the torque in the table.

    Step 3:

    Next, use the equation:

    \[\sum\,T=0\]

    To solve for the torque created by the muscle \(T_M\).

    Expand the equation to list all of the torques: \(T_M+T_D+T_S=0\).

    Isolate for the unknown muscle torque:

    $$T_M=T_D-T_S.$$Step 4:

    Fill in known values from the table you created above and then solve the problem: $$T_M=(-170\,\mathrm{Nm})-(-3.9\,\mathrm{Nm})=173.9\,\mathrm{Nm}$$The muscle must create a torque of \(173.9\, \mathrm{Nm}\) which is opposite in direction to the torques created by segment and dumbbell weights, to prevent angular acceleration.

    Step 5:

    Calculate the muscle force \((F_M)\) using this equation: \[T_M=F_M\,\times\,M_{\text{Arm}}\]

    Isolate for \(F_M\)

    Rearrange the equation: $$F_{\mathrm M}=\frac{T_{\mathrm M}}{M_{\mathrm{Arm}}}=\frac{173.9\;\mathrm{Nm}}{0.05\;\mathrm m}=3\,478\;\mathrm N$$

    Step 6:Finally, write your answer out:

    Muscle torque required to prevent rotation is \(3\,478\,\mathrm{N}\).

    Remember when you calculate a large force value from the muscle, the muscle force will be much larger than the force held in hand. This is because of the short moment arm for the muscle at the joint.

    Muscles - Key takeaways

    • Simple machines are devices with no, or very few, moving parts that make work easier.
    • A machine's ability to do work is measured by two factors: (1) mechanical advantage and (2) efficiency.
    • There are six types of simple machines: the wheel and axle, pulley, lever, wedge, inclined plane, and screw.
    • Muscles are an example of a type of simple machine called a lever.
    • A lever is a simple system consisting of a rigid arm used to provide a force to lift or move a load.
    • A lever is composed of a fulcrum, effort, and load.
    • There are three classes of levers called: first, second, and third class.

    • Muscle torque is the turning effect caused by the force applied by the muscles through a moment arm of a given length, at a given angle to the joint.

    • Examples of torque in the human body are: walking, turning your head, and rotating your hand.

    • Angle of pull is the angle between muscle insertion and bone.

    • To achieve maximal torque from a muscle, the joint must be positioned so that the muscle being worked has a 90° angle of pull on the extremity.


    References

    1. https://www.flickr.com/photos/26344495@N05/51265481840
    2. https://www.stockvault.net/photo/196311/muscles
    Frequently Asked Questions about Muscle Torque

    What is muscle torque?


    Muscle torque is the force applied by the muscles through a moment arm of a given length, at a given angle to the joint.

    What is peak torque of muscle?

    Peak torque is the single highest torque output of the joint produced by muscular contraction. 

    How do you measure muscle torque?

    Muscle torque is measured when you multiply force by moment arm.

    Do humans generate torque?

    Humans generate torque. An example would be when muscular forces in our bodies cause our blood to circulate.

    How is torque related to muscle actions?

    Torque is related to muscle actions because it helps to create movement in the joints.

    Test your knowledge with multiple choice flashcards

    What is the definition of simple machines?

    Is this definition true or false?Muscle torque is the force applied by the muscles through a moment arm of a given length, at a given angle to the joint. 

    A machine's ability to do work is measured by which two factors?

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