Ch.14

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?

*H = mk2ω* H=angular momentum m=mass K=m w= angular velocity *H=Iw* I=moment of inertia H= 0.8 x 6 *H= 4.8 kg.m2/s*

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.

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

What are the factors that change angular momentum? (Check all that apply.)

the magnitude and direction of an acting external torque the length of the time interval over which a torque acts

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?

960 kg.m2/s H=mk^2w

What is the formula for the moment of inertia for a single particle?

I = mr2

How is Newton's second law expressed algebraically in angular terms?

T = Iα

What is the formula for angular impulse?

Tt, where T is torque and t is time

A table tennis paddle is gripped with a radius of gyration of 0.15 m and has a moment of inertia of 0.00225 kg.m2. What is the mass of the paddle?

0.1 kg

1. Transverse 2. longitudinal 3. anteroposterior

1. frontal 2. vertical 3. sagittal

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.

Newton's second law

A net torque produces angular acceleration of a body that is directly proportional to the magnitude of the torque, in the same direction as the torque, and inversely proportional to the body's moment of inertia.

Newton's first law

A rotating body will maintain a state of constant rotational motion unless acted on by an external torque.

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.

______ force is also called center-seeking force.

Centripetal

The force directed toward the center of rotation for a body in rotational motion is known as ___________ or center-seeking force.

Centripetal force

Newton's third law

For every torque exerted by one body on another, there is an equal and opposite torque exerted by the second body on the first.

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.

A tennis racket is gripped with a radius of gyration of 0.6 m and has a moment of inertia of 0.108 kg.m2. What is the mass of the tennis racket?

I=mK^2 I= moment of inertia m=total body mass k= distance known as the radius of gyration m=0.3

A baseball bat has a mass of 0.9 kg and is gripped with a radius of gyration of 0.8 m. What is its moment of inertia?

I=mK^2 I= moment of inertia m=total body mass k= distance known as the radius of gyration 0.576 kg.m2

A baseball bat has a mass of 1.1 kg and a moment of inertia of 0.891 kg.m2. What is the radius of gyration?.

I=mK^2 I= moment of inertia m=total body mass k= distance known as the radius of gyration 0.891/1.1= .81 then take the square root of it =0.90

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=mk^2

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.

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?

The segments have heterogeneous mass distributions. The segments are of irregular shapes.

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. T/F

True this is obviously impractical. In practice, mathematical procedures are used to calculate the moment of inertia for bodies of regular geometric shapes and known dimensions.

What is the angular impulse when a torque of 13 N.m is applied to a system for 1.2 seconds? Multiple choice question.

Tt=△H 13 x 1.2= 15.6

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?

Tt=△H Tt=(Iw)^2 - (Iw)^1 7.8 x t= 39 t= 5 sec

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 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 ______.

bc r is always squared

On Earth, angular momentum is conserved whenever ______.

gravity is the only acting external force

Cat rotation is performed around the ______ axes of the two major body segments because it is easier to initiate rotation around these axes.

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?

positioning the body's mass away from the axis of rotation increasing the body's mass

In the formula I = mk2 to calculate the moment of inertia, what does the variable k represent?

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

______ 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

Identify the principal axes the human body moves around when it rotates free of support.

the sagittal axis the frontal axis the vertical axis