Biomechanics Ch 14 - (CONNECT)
The mass of a body is 6 kg, its angular velocity is 10 rad/s, and its radius of gyration is 4 m. What is its angular momentum?
(6)(4)^2 (10) = 960 kgm^2/s
A torque of 5 N.m is applied to a system for 0.2 seconds. What is the initial angular momentum of the system if its final moment of inertia is 0.4 kg.m2 and its final angular velocity is 2.5 rad/s?
0 kg.m2/s
A system has an angular impulse of 4.8 kg.m2/s. What is its initial moment of inertia if its initial angular velocity is 5 rad/s and its final angular momentum is 9.2 kg.m2/s?
0.88 kg.m2
A system has an angular impulse of 6.4 kg.m2/s. What is its final moment of inertia if its final angular velocity is 7 rad/s and its initial angular momentum is 2 kg.m2/s?
1.2 kg.m2
What is the angular impulse when a torque of 13 N.m is applied to a system for 1.2 seconds?
15.6 N.m.s
What is the torque that must be applied to a system for 4.6 seconds to obtain an angular impulse of 11.5 N.m.s?
2.5 N.m
A body's moment of inertia is 0.8 kg.m2, and its angular velocity is 6 rad/s. What is the angular momentum of the body?
4.8 kg.m2/s
For how long does a torque of 7.8 N.m need to be applied to a system to generate an angular impulse of 39 N.m.s?
5 sec
A 0.3 kg stone on a 0.5 m string is swung in circles and released with a tangential linear velocity of 35 m/s. What is the centripetal force of this system?
735 N
Cat rotation is accomplished most effectively when the two body segments are in a ______ pike position.
90°
Which of the following actions best exemplifies the transfer of angular momentum from one principal axis of rotation to another?
A diver transitions from a somersaulting rotation to a twisting one midair.
Which of the following statements are true of the principal axes?
All of them pass through the total-body center of gravity. The body can move around any of them when it is free of support.
Which of the following formulas is used to calculate angular momentum?
H = mk2ω
What do the letters in the formula H = Iω represent?
H represents angular momentum, I represents moment of inertia, and ω represents angular velocity.
What is the formula used to calculate the moment of inertia for a body of known mass such as segments of the human body or the body as a whole in different positions?
I = mk2
What is the formula for the moment of inertia for a single particle?
I = mr2
True or false: Assessing moment of inertia for a body with respect to an axis by measuring the distance of each particle of body mass from an axis of rotation and then applying the formula is impractical.
Reason: This is true. Assessing the moment of inertia for a body with respect to an axis by measuring the distance of each particle of body mass from an axis of rotation and then applying the formula is obviously impractical. In practice, mathematical procedures are used to calculate the moment of inertia for bodies of regular geometric shapes and known dimensions.
______ depends on both the amount of mass possessed by an object and the distribution of that mass with respect to the axis of rotation.
Resistance to angular motion
How is Newton's second law expressed algebraically in angular terms?
T =Ia
What happens to the angular momentum of a body when angular velocity is partially transferred from one principal axis of rotation to another in the absence of external forces of torque?
The angular momentum of the body remains constant.
When a volleyball player performs a spike, moving the hitting arm with a high angular velocity and a large angular momentum, a compensatory angular momentum is generated in the lower body (legs). Why is the angular velocity of the legs generated to counter the angular momentum of the swinging arm is much less than the angular velocity of the spiking arm?
The moment of inertia of the two legs with respect to the hips is much greater than that of the spiking arm with respect to the shoulder.
What is the relationship of the radius of gyration of an object with its radius of rotation?
The radius of gyration is always longer than the radius of rotation.
Why is it impractical to assess the moment of inertia for a body with respect to an axis by measuring the distance of each particle of body mass from an axis of rotation and then applying the formula? (Check all that apply.
The segments have heterogeneous mass distributions. The segments are of irregular shapes.
What is the principle of conservation of momentum for angular motion?
The total angular momentum of a given system remains constant in the absence of external torques.
What is the formula for angular impulse?
Tt, where T is torque and t is time
Change in angular momentum equal to the product of torque and time interval over which the torque acts is known as
angular impulse
In the formula for determining the resistance of a particle to angular acceleration, the radius of rotation of a particle changes as the ______ changes.
axis of rotation
The force directed toward the center of rotation for a body in rotational motion is known as ________or center-seeking force.
centripetal force
The force that prevents a rotating body from leaving its circular path while rotation occurs around a fixed axis is known as ______.
centripetal force
When a diver's body's principal moment of inertia is reduced during the execution of a one-and-a-half front somersault dive, there is a ______.
compensatory increase in angular velocity
When an airborne volleyball player with a total-body angular momentum of zero performs a spike, moving the hitting arm with a high angular velocity and a large angular momentum, there is a compensatory rotation of the lower body, producing a(n) ______.
equal amount of angular momentum in the opposite direction
On Earth, angular momentum is conserved whenever ______.
gravity is the only acting external force
Identify an anthropomorphic characteristic that is advantageous for sprinters and results in a smaller moment of inertia of the leg with respect to the hip.
having more massive thighs and slimmer lower legs
During sprinting, maximum angular acceleration of the ______ is desired.
leg
.Cat rotation is accomplished most effectively when the radius of gyration of one body segment is maximal with respect to the ______ axis of the other segment.
longitudinal
It is easier to initiate rotation about the ______ principal axis because total-body moment of inertia with respect to this axis is much smaller than the total-body moments of inertia with respect to the other two axes.
longitudinal
The moment of inertia of an entire body is the sum of the moments of inertia of all the ______ the body contains.
mass particles
Which of the following factors increase the resistance of a body to angular acceleration? (Check all that apply.)
positioning the body's mass away from the axis of rotation increasing the body's mass
The distribution of a body's mass with respect to the axis of rotation (r) is more important than the total amount of body mass (m) in determining resistance to angular acceleration because ______.
r is always squared
In the formula I = mk2 to calculate the moment of inertia, what does the variable k represent?
radius of gyration
The distance from an axis of rotation to a point at which the mass of a body can theoretically be concentrated without altering the inertial characteristics of the rotating body is known as the
radius of gyration
According to the principle of conservation of angular momentum, in a one-and-a-half front somersault dive, a diver leaves the springboard with a fixed amount of angular momentum that ______.
remains constant throughout the dive
Smaller gymnasts have ______, which give them an advantage in performing skills involving whole-body rotations, despite the fact that larger gymnasts may have greater strength and be able to generate more power.
smaller moments of inertia
Which of the following factors is the most influential factor on the magnitude of centripetal force as evident from its formulas?
speed of rotation
Which factor most dramatically influences the angular momentum of a body?
the distribution of the body's mass with respect to the axis of rotation
Identify the factors that influence the magnitude of the angular momentum of a body. (Check all that apply.)
the distribution of the body's mass with respect to the axis of rotation the angular velocity of the body the mass of the body
What are the factors that change angular momentum? (Check all that apply.)
the length of the time interval over which a torque acts the magnitude and direction of an acting external torque
During an airborne somersault, what are the two components of the angular momentum of a single segment with respect to the principal axis of rotation passing through the total body center of gravity?
the local term and the remote term
Identify the principal axes the human body moves around when it rotates free of support. (Check all that apply.)
the sagittal axis the vertical axis the frontal axis
True or false: Several prominent female gymnasts who achieved world-class status during early adolescence faded from the public view before reaching age 20 because of declines in their performance capabilities generally attributed to changes in body proportions with growth.
true
