Linear momentum (the quantity of motion that an object possesses) is the product of mass and _________.
What is "velocity?"
Inertial property for rotating bodies representing resistance to angular acceleration.
What is Moment of Inertia?
A rotating body will maintain a constant state of rotational motion unless acted upon by an external torque is the angular equivalent to this law.
What is "Newton's First Law of motion: a body at rest will stay at rest and a body in motion will remain in a constant state of motion unless acted upon by some external force?"
Force directed toward the center of rotation for a body in a rotational motion
What is Centripetal Force?
This is the distance from the axis of rotation to the CG.
What is "radius of rotation?"
Quantity of angular motion possessed by a body; measured as the product of moment of inertia and angular velocity
What is Angular Momentum?
Resistance to angular acceleration is directly proportional to it's _________ and the distance the _________ is distributed from the axis of rotation
What is "Mass?"
Linear measure Angular Equivalent
mass (m) moment of inertia (I)
force (F) ____________ (T)
momentum (M) angular momentum (H)
impulse (Ft) _______ impulse (Tt)
What are "torque" and "angular?"
Centripetal force is also known as this force because its direction is always constant.
What is "center-seeking force?"
When the entire human body rotates free of support, it moves around one of these three principal axes that are mutually perpendicular passing through the total body center of gravity.
What are "Transverse (or frontal)," the "AP (or sagittal)," and "Longitudinal (or vertical)" Axes?
These three factors affect the magnitude of a body's angular momentum.
What are "mass," "distribution of that mass with respect to the axis of rotation (radius of gyration)," and " the angular velocity of the body?"
H=mk2w
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
What is Bat A?
Newton's 2nd law of angular motion states: "A net torque produces angular acceleration of a body that is directly proportional to the __________ of the torque, in the same _________ as the torque, and ___________ proportional to the body’s moment of inertia
What are "magnitude," "direction," and "inversely?"
This is the most influential factor on the magnitude of centripetal force.
What is "speed of rotation?"
Fc=mrw2
This is the distance from the axis of rotation to a point where the body's mass could be concentrated without altering its rotational characteristics.
What is "radius of gyration?"
What is happening in terms of Conservation of Angular Momentum.
The amount of angular momentum a person being spun around remains constant throughout the spin.
As the person brings their arms in, the radius of gyration decreases, thereby decreasing the body's principal moment of inertia along the vertical axis...speeding the person up.
As the person extends their arms, the radius of gyration increases, thereby increasing the body's principal moment of inertia along the vertical axis...slowing the person down.
To decrease the moment of inertia (and to make it easier), Little League players often unknowingly do this when swinging a bat that is linger and/or heavier than they can realistically handle.
What is "choke up?"
Newton's 3rd law of angular motion states: For every torque exerted by one body on another, there is an __________________________________________ exerted by the second body on the first.
What is "equal and opposite torque"
DAILY DOUBLE!!
This fictional force where we feel pushed toward the outside of a rotating body (eg., car going around a curve) could be more appropriately described as the absence of centripetal force acting upon an object.
What is "centrifugal force?"
What is actually happening is, in accordance to Newton's First Law, the body's inertia tends to cause it to continue traveling on a straight, rather than curved, path. The car seat, seat belt, or door provide a reaction force that changes the direction of the body's motion.
Change in angular momentum equal to the product of torque and time interval over which the torque acts.
What is "Angular Impulse?"
When someone is doing a back flip into a pool, he or she can do this to change their angular momentum, thereby improving the dive.
What are "straighten the arms," "rotate the arms faster," or "bend the elbows."
"Magnitude and direction of the external torques," and "Length of time over which each torque acts?"
When we have an external torque that acts on angular momentum, it changes the amount of angular momentum present in the system predictably.
Tt=change in angular momentum
Distribution of mass, with respect to axis of rotation, is more important than total amount of body mass in determining resistance to angular acceleration.
_______________ is a characteristic fast sprinters possess to reduce moment of inertia (so they can maximize angular motion).
What is "extreme flexion of the knee while running"
-or-
What are "bigger thighs and smaller lower legs?"
When a baseball player forcefully swings a bat, rotating the mass of the upper body, a torque is created around the player's longitudinal axis.
If the batter's feet are not firmly planted, the lower body tends to rotate around the longitudinal axis in the opposite direction.
This is an example of what angular analogue of Newton's Laws of Motion.
What is "Third Law?"
Centripetal force = mv2/r, where "m" is the mass [of the mud], "v" is the tangential velocity [of the mud], and "r" is the radius of the rotation.
Explain, how mud stuck on a rotating wheel would remain stuck longer as a vehicle increases it's speed.
What is "put bigger wheels on the vehicle" or "increase the mass of the mud" or "keep the vehicle's speed lower"