KINE 3050 Angular Kinetics

Torque is the tendency to produce a change in

rotational motion

Torque is determined by

Magnitude of applied force

Direction of applied force

Location of applied force

Force is a

action that creates changes in linear motion

What is required to rotate an object

torque 

Torque is created by

force and depends on 

• where the force is applied

• the point which the object rotates

Torque is a vector or scalar?

Vector

What are the signs of torque

Counterclockwise → positive

Clockwise → negative

Classic example of torque force is

how you open a door

• hinges of door is axis of rotation

• open door closer or further from the hinges

What are the units of torque and the equation

Torque (τ) created by a force = to the lever arm (d) x the magnitude of the force (F)

units : N/m

What is the center of rotation?

point or line about which an object turns

ex) doors center of rotation is the hinges

A force applied far from the center of rotation produces a 

greater torque than a force applied close to the center of rotation 

Torque is created when the line of action of a force

DOES NOT pass through the center of rotation

Line of action is an

imaginary line of indefinite length drawn along the direction of the force

The brachialis muscle is 

a large muscle, but it has the smallest moment arm

(poorest mechanical advantage) 

The biceps brachii

large cross section and has a longer moment arm

The brachioradialis has

a smaller cross section and the longest moment arm

( best mechanical advantage )

If the force due to the biceps shown is 100N and the moment arm is 1.5cm. What is the torque produced by the biceps 

T = 100N (1.5cm)

Step 1 : Convert 

100N (0.015m) 

Step 2: Solve

Answer: 1.5N/m 

The application is: During a concentric bicep curl, where the bicep brachii is producing 100N of force, there is 1.5N/m of torque force (rotational force) at the elbow joint

A muscle with a small moment arm needs to produce

more force to generate the same torque as a muscle with a larger moment arm

Although human motion is general (translation and rotation), it is generated by

a series of torques and rotations

Lines of action of muscle forces

DO NOT pass through the joints’ axes of rotation

The moment arm is the

shortest distance from a forces line of action to the axis of rotation

• always perpendicular to the line of action and passes through the axis of rotation

The magnitude of the moment arm of the biceps muscle changes

throughout the range of motion

Computing the moment arm is determined by

distance from axis of rotation to point at which force is applied

and 

angle at which the force is applied 

An 80N force acts at the end of a 12cm wrench as shown. What is the torque ? 

Torque = f(d) = N/m (Answer will be +)

F=80N

MA= ?

Theta Angle = 60 degrees 

Step 1: Find moment arm = 0.104m

Step 2: Solve = 80N x 0.104m

Answer: 8.32N/m

The center of mass is the point in a body or system

where the entire mass may be assumed to be concentrated

• imaginary point in space

• not a physical activity

• not a fixed point (changes when parts of an object change position)

The force of gravity acts

downward through the center of mass

Which of the following can be determined by taking the absolute value of the ratio of the velocity of separation to the velocity of approach?

Coefficient of Restitution 

Stability is directly

proportional to the area of the best on which the body rest

• in a given direction is directly proportional to the horizontal distance of the center of gravity from that edge of the base

• directly proportional to the weight of the body

• indirectly proportional to the distance of the body above the base 

What does stability depend on?

State of equilibrium : balanced and forces are =

Gravity: attraction between earth and object

Gravitational Force: Directed vertically downward

Center of Gravity: Balance point of object with torque equal on all sides

Base of Support: Part of body in contact with support surface

Line of Gravity: imaginary vertical line passing through center of gravity towards earth

The outcome of torque is to produce

a rotation about an axis

Lever is a rigid

rod that is rotated about a fixed point or axis 

What are the components of levers?

• Resistance/Load Arm

• Effort force

• Effort/Load Arm

• Fulcrum Arm

Levers are a simple

machine consisting of a relatively rigid bar-like body that can be made to rotate about an axis or fulcrum

Classification depends on

relative position of the force, applied force, and fulcrum

• 1st class

• 2nd class

• 3rd class

The interaction between internal and external forces in levers ultimately controls

movement

• These forces interact through a system of bony levers, with the pivot point located at the axis of rotation of our joints

• Through these systems of levers, the internal and external forces are converted to internal and external torques, which ultimately cause movement (or rotation) of our joints

Mechanical Advantage is the 

ratio of effort arm to resistance arm 

Levers will either favor

power OR distance but never both

• any advantage gained in power is lost in distance and vice versa

The arrangement of axis in relation to force and the resistance determines?

the type of lever

Longer the FA, easier to move : With a longer FA, the part will be easier to move, but the FA will have to move a greater distance

Longer the RA, harder to move: With a longer RA, won’t have to move as far, but it will be harder to move

First class levers have the fulcrum located 

between the load and the effort 

• very useful for lifting large loads with little effort 

A teeter-totter, car jack, and crowbar are examples of what class lever

First Class

Second class levers load is located

between the effort and the fulcrum

• easy to move objects over distance

Wheelbarrow, bottle opener, and a oar are examples of what class lever?

Second Class

In a third class lever, the effort is located between the

load and the fulcrum

• good for making precise movements

Pair of tweezers, swinging a baseball bat, and using your arm to lift something are examples of what class lever?

Third Class

What lever class

1st class

What class lever?

2nd class

What class lever?

3rd class