Download the App!

Get 24/7 study help with the Numerade app for iOS and Android! Enter your email for an invite.

$\cdot$ The spinning figure skater. The outstretched hands and arms of a figure skater preparing for a spin can be considered a slender rod pivoting about an axis through its center. (See Figure $10.53 .$ ) When the skater's hands and arms are brought in and wrapped around his body to execute the spin, the hands and arms can be considered a thin-walled hollow cylinder. His hands and arms have a combined mass of 8.0 $\mathrm{kg}$ . When outstretched, they span 1.8 $\mathrm{m}$ ; when wrapped, they form a cylinder of radius 25 $\mathrm{cm} .$ The moment of inertia about the axis of rotation of the remainder of his body is constant and equal to 0.40 $\mathrm{kg} \cdot \mathrm{m}^{2} .$ If the skater's original angular speed is 0.40 $\mathrm{rev} / \mathrm{s}$ what is his final angular speed?

Get the answer to your homework problem.

Try Numerade free for 7 days

Like

Report

1.14 rev/s

Physics 101 Mechanics

Chapter 10

Dynamics of Rotational Motion

Newton's Laws of Motion

Rotation of Rigid Bodies

Equilibrium and Elasticity

University of Washington

Hope College

University of Sheffield

Lectures

02:34

In physics, a rigid body is an object that is not deformed by the stress of external forces. The term "rigid body" is used in the context of classical mechanics, where it refers to a body that has no degrees of freedom and is completely described by its position and the forces applied to it. A rigid body is a special case of a solid body, and is one type of spatial body. The term "rigid body" is also used in the context of continuum mechanics, where it refers to a solid body that is deformed by external forces, but does not change in volume. In continuum mechanics, a rigid body is a continuous body that has no internal degrees of freedom. The term "rigid body" is also used in the context of quantum mechanics, where it refers to a body that cannot be squeezed into a smaller volume without changing its shape.

02:21

In physics, rotational dynamics is the study of the kinematics and kinetics of rotational motion, the motion of rigid bodies, and the about axes of the body. It can be divided into the study of torque and the study of angular velocity.

11:43

The Spinning Figure Skater…

05:00

I The spinning figure skat…

04:08

The outstretched hands and…

04:57

01:54

03:20

01:29

On average, both arms and …

A reasonable estimate of t…

05:28

The 165 -lb ice skater wit…

01:51

$\|$ Ice skaters often end…

03:32

Calculate the moment of in…

According to conservation law of angular momentum, we know the initial angular momentum should be equal to the final momentum, which is l. I o l f here. If we expand it, we have. I i omega is equal if omega f. I is the initial moment of inertia. Omega is the initial angular velocity, and i f is the final number of inertia. Omega f is the final angular velocity. If we do some arrangement here, we'll have the final angular velocity or not tower final angular speed is equal to i i omega i over. If so, the initial moment of inertia should be got, i 0 plus 1 over solve times m and 10 times 1 square. I 0 see the moment inertia of the skater and then 1 half i'm sorry, 1. Over 12 m r 1 square is the moment of inertia of the action that scattered took first because initially the skater was prepared to spin like a slender rod, and we know the moment of inertia of the slender rod is 1 half 1 square. If we plug in the values we have, i, i is equal to 0.4 kilo gram, his meter square plus 112 times 8 kilogram and then times 1.8 meter to the power 2 point. So eventually we have. The initial moment of inertia is equal to 2.56 kilo. Gram has meter square and then, let's take a look at the final moment of inertia, which is equal to 0 plus m r 2 square m r 2 square. Here is the moment of inertia of the cylinders, since eventually when, when we wrap lay, they form a cylinder of radius of 25 centimeter. So, therefore, if you're plugging back to the equation with these values, here we'll have, i f is equal to 0 point 4 kilo. Gram 10 meter square plus 80.25 meter to the power of 2. So we know 0. Point 25 meter here is actually 25 centimeter. Okay. So therefore, eventually we'll have. The final moment of inertia is 0 point. 9 kilo. Grain has a meter square and we know the initial angular speed is 0.4 revolution per second. So therefore, we can determine the final angular speed and we use a black pencil to have omega f is equal to i i omega, which is 2.56 kilties, meter square and then times 3.4 revolution per second and then over. If which is 0.9 kilo times meter square- and this will give us the final angular speed is about 1.14 revolution per second, and this is the answer for this question.

View More Answers From This Book

Find Another Textbook

Numerade Educator

02:01

'10) (maximum) 1 (IAXimuI True current currelse ; False the the circuit…

03:23

'QUESTION10 points Save Answer11.28 part a pendulum makes 36 vi…

01:09

'The drawings show two examples which ray of light iS refracted at the …

03:39

'#81.A 205-kg log is pulled up ramp by means of & rope that iS para…

03:04

'An object is positioned 26 cm from spherical concave mirror of unknown…

02:05

'You are attempting to create standing wave with n = 7 in a pipe 0.50 m…

03:05

'Problem#}Determine the vertical clamping force at E in terms of th…

05:22

'001 (part 1 of 2) 10.0 pointsObjects with masses of 128 kg and 637…

02:09

'15. What is the rest energy of an electron, given its mass is 9.11X10 …

03:10

'10.Assuming You are playing the pirates game On computer_ CHnOn on top…