Exam 3 & Final Flashcards
What is “Pure Rotation”?
A term used when there is no linear motion of the axis of rotation.
What is “General Motion”?
When rotation and translation occur at the same time.
When you are closer to the joint do you have more or less linear rotation?
You will have less linear rotation when you are closer to the joint. Points further from the axis travel more.
Do points on an axis of rotation travel?
No, unless there is general motion occuring.
What are the angle measurements for angular kinematics?
Degrees, radians (57.3°/rad = 180/π)
Is angular position (𝚯) a scalar or vector quantity?
It is a vector orientation relative to positive x-axis. 𝚯
What plane of axis does angular rotation occur?
If an object is moving in the x,y plane, the axis for the vector is z.
𝛳= 30°k
What is “Angular Displacement”?
It is the final position minus the initial position.
Δ𝛳= 𝛳f-𝛳i
What is “Angular Distance”?
It is the angular length of path traveled.
𝛳1 + 𝛳2
What is “Angular Velocity”?
The time rate at which an object rotates or revolves about an axis. ⍹ = average angular velocity = ▵𝛳/▵t
What is “Angular Acceleration”?
A change in angular velocity of an object per unit of time. ⍶ = average angular acceleration = ▵⍹/▵t
Does a positive average angular velocity (⍹) guarantee a positive average angular acceleration (⍶)?
No, just like linear acceleration, things can be positive in the negative direction.
Is angular speed a vector or scalar quantity?
It is a scalar quantification of how fast an object is rotating independent of direction.
Is angular speed a positive, negative, or zero value?
Angular speed is always a positive value.
What is “Instantaneous Angular Speed”?
It is the magnitude of the instantaneous angular velocity vector (⍹)
What is “Average Speed”?
It is the magnitude of the average angular velocity vector (⍹), but it could also be the angular distance/time.
What is “Angular Speed”?
It is a scalar quantification of how fast an object is rotating independent of direction.
Can you determine 𝚯, ⍵, ⍺ curves from one another?
Yes, just like linear PVA, you can find the instantaneous in the slope of a line.
What are “Segment Angles”?
They describe orientation of a body segment. They are typically measured from horizontal axis at distal end. They are positive in the CCW direction.
How to solve for segment angles
Set up right triangles with known side lengths using the coordinate data. Solve for appropriate angles in triangles, and adjust if needed.
𝛳thigh = 𝛳+90°
𝛳thigh = tan^-1(▵x/▵y) + 90° = 105°
T or F
Your forearm and hand rotate about the elbow as you flex the joint. Assuming pure rotation about the elbow, the COM of your forearm and the COM of your hand will go through the same angular change but they will go through different linear change in position.
True
T or F
When referring to the rotation of an object as “pure” rotation we are conveying that there is no change in the radius (length) of the object relative to its axis of rotation.
False
T or F
A radian is a unitless quantity, coming from the ratio of the arc length of a circle divided by the radius of the circle
True
T or F
Pi radians = 360 degrees
False
T or F
While PVA are vector quantities, the angular variables 𝚯, ⍵, ⍺ are scalar quantities
False
T or F
Similar to reporting a positive polar orientation of a vector as CCW, 𝚯⍵⍺ are also positive CCW relative to our positive x-axis
True
T or F
An object is changing orientation in the x-y plane making the rotation about the z-axis
True
T or F
While linear distance traveled of an object is always 0 or positive, the angular distance traveled of an object can be 0, +, or -
False
T or F
An object has negative angular acceleration. This means it is either speed up while rotating in the negative direction or slowing down while rotating in the positive direction
True
T or F
For a given radius of an object traveling on a circular path, doubling the angular velocity will double the centripetal acceleration. However, doubling the angular acceleration will quadruple the tangential acceleration
False
T or F
Centripetal and centrifugal are interchangeable terms, both referring to the linear acceleration of an object towards the axis of rotation
False
T or F
When performing the up phase of the biceps curl, beginning and ending with a pause, we would expect the magnitude of the centripetal acceleration of the barbell rotating about the elbow joint to first increase then decrease, reaching a peak near the middle of the up phase when the forearm is horizontal.
True
T or F
The instantaneous linear velocity of a point on a rotating object will always be tangent to the path. However, the resultant linear acceleration is not always perpendicular to the path
True
T or F
The body segment from the elbow joint to wrist joint is technically the “arm” segment. However, for clarity, we typically refer to it as the “forearm”.
False
T or F
Segment angles are measured relative to the proximal end of a segment for the upper and lower extremities
False
Your segment angle vs time profile is a hill. We would expect the segment angular velocity vs time profile to be a ________
Hill-Valley
Joint angles can be calculated from _______
Known segment angles proximal and distal to the joint, and joint coordinate data and the Law of Cosines.
T or F
The included elbow joint angle will increase as you flex the joint and the excluded elbow joint angle will decrease as you flex the joint
False
In the Mimi et al (2004) article segment/joint angle definitions discussed in lecture, which were consistent with how we would want to define and name them
Knee angle
T or F
You roll two balls (without slipping). One has twice the radius as the other. For the same linear velocity of their COM, the ball with the smaller radius will have twice the angular velocity. However, the relationship between the radius of the ball and the angular velocity of the rolling ball is non-linear
True
What are the SI units for Torque (T)?
The SI units for Torque (T) are Nm. 1Nm = .7376ftlb
What does “Torque” do?
Torque (T) is the effect of a force that tends to cause a change in a body’s state of angular position or motion.
What else is Torque referred as?
It is also known as “moment” or “moment of force”. In biomechanics “moment” is typical and “M” is the variable.
What is the variable for “Moment”?
The variable for “moment” is “M”
What is “Torque”?
It is equal to the product of the magnitude of force (F) and its moment arm (r) with respect to the axis of rotation.
Is “Torque” a scalar or vector quantity?
Torque is technically a vector about the axis perpendicular to the plane of the force and moment arm.
What direction will indicate positive and negative torque.
CCW torque is positive. CW torque is negative.
What is a “Moment Arm”?
A moment arm (r) is perpendicular distance between the line of action of the force and the axis of rotation of the object.
How do you calculate torque?
Treat F and r as positive values, then assign +/- based on sense of turning.
Why do we want to avoid the term “Lever Arm”?
Some define it synonymous with moment arm, others define it as the distance from the axis of rotation to the point of application of the force. It’s too unclear to use them interchangeably.
Can torque be a vector cross product?
Yes, one vector is the force and the other is a displacement vector. The displacement goes from the axis of rotation to point of application of the force. It is a very complicated way to calculate.
Resultant vs Resolved Force for Torque
Torque calculated from the resultant force will equal the sum of the torques produced by the individual components of the resultant force.
1 ftlb of torque is _____ 1Nm of torque
Greater than (1Nm = .7376 ftlb)
T or F
Torque is often referred to as a “moment” or “moment of force” in biomechanics with an “M” used as the variable instead of a “T”. However, we will be sticking to referring to it as Torque and the variable “T” to avoid confusion.
True
T or F
Torque is a scalar quanitity that may either be positive or negative base on the direction of rotation that it will produce.
False. Torque is a vector.
T or F
When calculating torque you want to multiply the magnitude of the force with the length of the moment arm (both positive) and then assign it positive if it tends to rotate an object CW and negative if it rotates CCW when using our standard Cartesian coordinate system.
False
T or F
While some refer to the moment arm as the lever arm, not everyone defines the lever arm this way. Some define the lever arm as the straight line distance from the axis of rotation to the point of application of the force on the object. As such, it is best to avoid using the term lever arm.
True
T or F
The moment arm is the perpendicular distance (length) between the line of action of the force and the axis or rotation. As such, a vertical force will have a horizontal moment arm and a horizontal force will have a vertical moment arm.
True
You’re working with the vertical force applied to your hand (FHy). The moment arm for this force relative to the axis of rotation should be labeled_____
rHy (r subscript Hy)
T or F
While not an intuitive way to calculate torque, it can be calculated as Fdsin𝛳. If the proper vector d and angle 𝛳 are selected, dsin𝛳 will equal the length of the moment arm.
True