Quiz 3

What is the general location of the center of gravity of the human body?

57% of the height for men, and 55% of the height for women.

Radius of Gyration

A length measurement that represents how far from the axis of rotation all of the object's mass must be concentrated to create the same resistance to change in angular motion as the object had in its original shape.

Radian (rad)

A ratio of arc length divided by the radius.

Centripetal Acceleration

Acceleration of an object toward the center of a curved or circular path.

If a net external force acts on a body, the acceleration caused by this new force is?

Acceleration of center of gravity.

Eccentric Axis

An axis that does not pass through the implement's center of gravity.

How do changes in angular momentum affect angular velocity?

Angular momentum remains the same, so the reduction in the moment of inertia must be accompanied by an increase in angular velocity.

What does a decrease in moment of inertia cause in order to keep angular momentum constant?

Any decreases in moment of inertia created by the person bringing limbs closer to the axis of rotation require increases in angular velocity to keep angular momentum constant.

What does an increase in moment of inertia cause in order to keep angular momentum constant?

Any increases in moment of inertia created by the person moving limbs father from the axis of rotation cause decreases in angular velocity to keep angular momentum constant.

What is the relationship between a body's moment of inertia and it's angular velocity?

Because the body's moment of inertia is variable and can be changed by altering limb positions, the body's angular velocity also changes to accommodate the changes in the moment of inertia.

Center of Mass vs. Center of Gravity

Center of mass is based on mass, whereas center of gravity is based on weight. When the gravitational field across an object is uniform (on Earth), then the two are identical. Thus, if on Earth center of mass and center of gravity are equivalent terms and can be used interchangeably.

What is the relationship between centripetal acceleration and tangential linear and angular velocity?

Centripetal acceleration is directly proportional to the square of tangential linear velocity and the square of angular velocity.

Angular Interpretation of Newton's 3rd Law

For every torque exerted by one object on another, the other object exerts an equal torque back on the first object but in the opposite direction.

Instantaneous Angular Velocity

How fast something is rotating at a specific instant in time. An indicator of how fast something is spinning at a specific instant in time.

Why do we care about stability?

In many sports and human movement activities, we want to be very stable because we increase our performance accuracy if we adopt stable positions.

Angular Interpretation of Newton's 1st Law

The angular momentum of an object remains constant unless a net external torque is exerted on it. The angular velocity remains constant. Its rate of rotation and its axis of rotation do not change unless an external torque acts to change it.

How does the angular version of Newton's 1st Law apply to the human body?

The angular momentum of the human body is constant unless external torques act on it for a single rigid body.

Angular Momentum

The product of moment of inertia and angular velocity. It has the same direction as the direction of the angular velocity. In summary, moment of inertia in angular motion is equivalent to mass in linear motion.

Angular (Rotary) Inertia

The property of an object to resist changes in its angular motion.

Angular Velocity

The rate of change of angular displacement. Units include radians per second, degrees per second, and revolutions per minute.

Angular Acceleration

The rate of change of angular velocity. Occurs when something spins faster and faster, or slower and slower, or when the spinning object's axis of spin changes direction. Units include radians per second squared and degrees per second squared.

Mass Centroid

The point where the mass of an object is balanced in all directions.

What do we need center of gravity for?

It makes us analyze human movement easier.

What does Newton's 1st Law require and not require?

It requires that the product of the moment of inertia times the angular velocity be constant if no external torques act. It does NOT require that the angular velocity be constant.

What is the effects of larger torques on angular momentum?

Larger torques can be created by using longer moment arms, and a larger external torque acting over a longer duration will create a larger change in angular momentum.

What is the relationship between tangential and linear acceleration?

Linear acceleration tangent to the path of rotation of a point occurs if the rotating object is being accelerated angularly.

How does center of gravity change with movement?

Location of center of gravity depends on the position of the limbs. Movement of any segment of the body causes center of gravity to shift in the same direction.

Stability

The capacity of an object to return to equilibrium or to its original position after it has been displaced.

Angular Displacement

The change in absolute angular position experienced by a rotating line (an object when the object is not a line). The angle formed between the final position and the initial position of a rotating line.

Angular Interpretation of Newton's 2nd Law

The change in angular momentum of an object is proportional to the net external torque exerted on it, and this change is in the direction of the net external torque.

Angular Impulse

The change in angular momentum. Provides us with the final outcome of external torques acting on an athlete or implement over some duration of time.

Tangential Acceleration

The component of linear acceleration tangent to the circular path of point on a rotating object. A line is tangent to a circle if the line intersects the circle at just one point. A line from this point to the center of the circle (a radial line) is perpendicular to the tangent line.

What factors affect stability?

The height of the center of gravity. The size of the base of support. The weight of the object.

What is the relationship between linear and angular velocity?

The instantaneous linear velocity of a point on a rotating object is equal to the instantaneous angular velocity of the rotating object times the radius.

What is the relationship between angular displacement and arc length?

The linear distance traveled is equal to the product of the angular displacement and the radius. The larger radius causes the arc length to be longer.

Center of Gravity

The location in space where the weight (gravitational force) of an object can be considered to act. The point in a body around which its weight is evenly distributed or balanced and through which the force of gravity acts. All the linear forces acting on the body must be balanced, and all the rotary forces must be balanced.

What factors affect the angular inertia?

The mass of an object. How the mass is distributed relative to the axis of rotation.

What is one advantage of muscle insertions being close to joints?

The muscle has to contract and shorten only a short distance to produce a large movement (linear displacement) at the end of the limb. Small movements of the hands produce large linear displacements.

What happens if an object is unconstrained and free to rotate about any axis?

The object will rotate about an axis through its center of gravity.

Angular Position

The orientation of a line with another line or plane.

Relative Angular Position

The other line or plane is capable of moving (e.g. angles formed by limbs at joints describe angular positions of limbs).

Absolute Angular Position

The other line or plane is fixed and immovable relative to the earth (e.g. the angle your forearm makes with a horizontal plane).

What is the relationship between radius and linear speed?

The point farther from the axis of rotation must have a fast linear speed because it moves a longer distance but in the same time.

Center of Mass

The point that represents the total mass distribution of a body.

What does it help to estimate angular momentum of our body?

The sum of the angular momenta of all the body segments gives an approximation of the angular momentum of the entire body.

What if tangential linear velocity is held consistent?

Then αT is inversely proportional to the r.

What if ω is held consistent?

Then αT is proportional to the r.

Factors of the Angular Interpretation of Newton's 3rd Law

Torques acting on the two objects have the same axis of rotation. The effects of these torques are different because they act on different objects. The effects of torques - related to the moment of inertia.

What is the relationship between angular and linear acceleration?

When the angular velocity of a spinning object increases, the linear velocity of a point on the object increases as well.

Does a point on a rotating object experience any linear acceleration if the object spins at a constant angular velocity with no angular acceleration?

Yes, remember that linear acceleration occurs if something speeds up, slows down, or changes direction. A point on an object spinning at constant angular velocity doesn't speed up or slow down, but because the point follows a circular path, it is constantly changing direction and is thus experiencing a constant linear acceleration.