Torque measures how a force causes an object to rotate.
Think about using a wrench to tighten a bolt. The torque
applied to the bolt depends on how hard we push the wrench (force) and how far up the handle we apply the force (distance). The torque increases with a greater force on the wrench at a greater distance from the bolt. Common units of torque are the newton-meter or foot-pound. Although torque is dimensionally equivalent to work (it has the same units), the two concepts are distinct. Torque is used specifically in the context of rotation, whereas work typically involves motion along a line.
Evaluating torque
A bolt is tightened by applying a force of
N to a 0.15-m wrench (
[link] ). The angle between the wrench and the force vector is
Find the magnitude of the torque about the center of the bolt. Round the answer to two decimal places.
Torque describes the twisting action of the wrench.
Substitute the given information into the equation defining torque:
The cross product
of two vectors
and
is a vector orthogonal to both
and
Its length is given by
where
is the angle between
and
Its direction is given by the right-hand rule.
The algebraic formula for calculating the cross product of two vectors,
is
The cross product satisfies the following properties for vectors
and scalar
The cross product of vectors
and
is the determinant
If vectors
and
form adjacent sides of a parallelogram, then the area of the parallelogram is given by
The triple scalar product of vectors
and
is
The volume of a parallelepiped with adjacent edges given by vectors
is
If the triple scalar product of vectors
is zero, then the vectors are coplanar. The converse is also true: If the vectors are coplanar, then their triple scalar product is zero.
The cross product can be used to identify a vector orthogonal to two given vectors or to a plane.
Torque
measures the tendency of a force to produce rotation about an axis of rotation. If force
is acting at a distance
from the axis, then torque is equal to the cross product of
and
Key equations
The cross product of two vectors in terms of the unit vectors
For the following exercises, the vectors
and
are given.
Find the cross product
of the vectors
and
Express the answer in component form.
In the following exercises, vectors
and
are given. Find unit vector
in the direction of the cross product vector
Express your answer using standard unit vectors.
Questions & Answers
I'm interested in biological psychology and cognitive psychology
Communication is effective because it allows individuals to share ideas, thoughts, and information with others.
effective communication can lead to improved outcomes in various settings, including personal relationships, business environments, and educational settings. By communicating effectively, individuals can negotiate effectively, solve problems collaboratively, and work towards common goals.
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miss
Every time someone flushes a toilet in the apartment building, the person begins to jumb back automatically after hearing the flush, before the water temperature changes. Identify the types of learning, if it is classical conditioning identify the NS, UCS, CS and CR. If it is operant conditioning, identify the type of consequence positive reinforcement, negative reinforcement or punishment
nature is an hereditary factor while nurture is an environmental factor which constitute an individual personality. so if an individual's parent has a deviant behavior and was also brought up in an deviant environment, observation of the behavior and the inborn trait we make the individual deviant.
Samuel
I am taking this course because I am hoping that I could somehow learn more about my chosen field of interest and due to the fact that being a PsyD really ignites my passion as an individual the more I hope to learn about developing and literally explore the complexity of my critical thinking skills