# 10.3 Dynamics of rotational motion: rotational inertia  (Page 5/8)

 Page 5 / 8

Calculate the moment of inertia of a skater given the following information. (a) The 60.0-kg skater is approximated as a cylinder that has a 0.110-m radius. (b) The skater with arms extended is approximately a cylinder that is 52.5 kg, has a 0.110-m radius, and has two 0.900-m-long arms which are 3.75 kg each and extend straight out from the cylinder like rods rotated about their ends.

The triceps muscle in the back of the upper arm extends the forearm. This muscle in a professional boxer exerts a force of $\text{2.00}×{\text{10}}^{3}\phantom{\rule{0.25em}{0ex}}\text{N}$ with an effective perpendicular lever arm of 3.00 cm, producing an angular acceleration of the forearm of $\text{120}\phantom{\rule{0.25em}{0ex}}{\text{rad/s}}^{2}$ . What is the moment of inertia of the boxer’s forearm?

$\text{0.50 kg}\cdot {\text{m}}^{2}$

A soccer player extends her lower leg in a kicking motion by exerting a force with the muscle above the knee in the front of her leg. She produces an angular acceleration of $30.00 rad/{\text{s}}^{2}$ and her lower leg has a moment of inertia of $\text{0.750 kg}\cdot {\text{m}}^{2}$ . What is the force exerted by the muscle if its effective perpendicular lever arm is 1.90 cm?

Suppose you exert a force of 180 N tangential to a 0.280-m-radius 75.0-kg grindstone (a solid disk).

(a)What torque is exerted? (b) What is the angular acceleration assuming negligible opposing friction? (c) What is the angular acceleration if there is an opposing frictional force of 20.0 N exerted 1.50 cm from the axis?

(a) $50.4 N\cdot \text{m}$

(b) $\text{17.1}\phantom{\rule{0.25em}{0ex}}{\text{rad/s}}^{2}$

(c) $17.0\phantom{\rule{0.25em}{0ex}}{\text{rad/s}}^{2}$

Consider the 12.0 kg motorcycle wheel shown in [link] . Assume it to be approximately an annular ring with an inner radius of 0.280 m and an outer radius of 0.330 m. The motorcycle is on its center stand, so that the wheel can spin freely. (a) If the drive chain exerts a force of 2200 N at a radius of 5.00 cm, what is the angular acceleration of the wheel? (b) What is the tangential acceleration of a point on the outer edge of the tire? (c) How long, starting from rest, does it take to reach an angular velocity of 80.0 rad/s?

Zorch, an archenemy of Superman, decides to slow Earth’s rotation to once per 28.0 h by exerting an opposing force at and parallel to the equator. Superman is not immediately concerned, because he knows Zorch can only exert a force of $4.00×{\text{10}}^{7}\phantom{\rule{0.25em}{0ex}}\text{N}$ (a little greater than a Saturn V rocket’s thrust). How long must Zorch push with this force to accomplish his goal? (This period gives Superman time to devote to other villains.) Explicitly show how you follow the steps found in Problem-Solving Strategy for Rotational Dynamics .

$3\text{.}\text{96}×{\text{10}}^{\text{18}}\phantom{\rule{0.25em}{0ex}}\text{s}$

or $1.26×{\text{10}}^{\text{11}}\phantom{\rule{0.25em}{0ex}}\text{y}$

An automobile engine can produce 200 N ∙ m of torque. Calculate the angular acceleration produced if 95.0% of this torque is applied to the drive shaft, axle, and rear wheels of a car, given the following information. The car is suspended so that the wheels can turn freely. Each wheel acts like a 15.0 kg disk that has a 0.180 m radius. The walls of each tire act like a 2.00-kg annular ring that has inside radius of 0.180 m and outside radius of 0.320 m. The tread of each tire acts like a 10.0-kg hoop of radius 0.330 m. The 14.0-kg axle acts like a rod that has a 2.00-cm radius. The 30.0-kg drive shaft acts like a rod that has a 3.20-cm radius.

Starting with the formula for the moment of inertia of a rod rotated around an axis through one end perpendicular to its length , prove that the moment of inertia of a rod rotated about an axis through its center perpendicular to its length is . You will find the graphics in [link] useful in visualizing these rotations.

$\begin{array}{c}{I}_{\text{end}}={I}_{\text{center}}+m{\left(\frac{l}{2}\right)}^{2}\\ \text{Thus,}\phantom{\rule{0.25em}{0ex}}{I}_{\text{center}}={I}_{\text{end}}-\frac{1}{4}{\text{ml}}^{2}=\frac{1}{3}{\text{ml}}^{2}-\frac{1}{4}{\text{ml}}^{2}=\frac{1}{\text{12}}{\text{ml}}^{2}\end{array}$

Unreasonable Results

A gymnast doing a forward flip lands on the mat and exerts a 500-N ∙ m torque to slow and then reverse her angular velocity. Her initial angular velocity is 10.0 rad/s, and her moment of inertia is $0.050\phantom{\rule{0.25em}{0ex}}\text{kg}\cdot {\text{m}}^{2}$ . (a) What time is required for her to exactly reverse her spin? (b) What is unreasonable about the result? (c) Which premises are unreasonable or inconsistent?

(a) 2.0 ms

(b) The time interval is too short.

(c) The moment of inertia is much too small, by one to two orders of magnitude. A torque of $\text{500 N}\cdot \text{m}$ is reasonable.

Unreasonable Results

An advertisement claims that an 800-kg car is aided by its 20.0-kg flywheel, which can accelerate the car from rest to a speed of 30.0 m/s. The flywheel is a disk with a 0.150-m radius. (a) Calculate the angular velocity the flywheel must have if 95.0% of its rotational energy is used to get the car up to speed. (b) What is unreasonable about the result? (c) Which premise is unreasonable or which premises are inconsistent?

(a) 17,500 rpm

(b) This angular velocity is very high for a disk of this size and mass. The radial acceleration at the edge of the disk is>50,000 gs.

(c) Flywheel mass and radius should both be much greater, allowing for a lower spin rate (angular velocity).

I need someone to explain how white light disperses to form the "ROYGBIV".
when it pass through a glass prism through a process called dispersion of light
Mahmud
What is an atom
An atom is the smallest indivisible particle of an element
Dera
When a toilet is flushed or a sink is drained, the water (and other material) begins to rotate about the drain on the way down. Assuming no initial rotation and a flow initially directly straight toward the drain, explain what causes the rotation and which direction it has in the northern hemisphere.
find the change in entropy of a 2.00 kg block of gold at 1063^0C when it meets to become liquid gold at 1063^0C
if you are asked to make a very sensitive thermometer which of the following fluids would you choose
precious
between mercy and gasoline
precious
it good to use mercury because mercury does not wet glass and it does not evaporate easily
Desmond
0
firdaus
SFAR Sifar SIFAT -<SIFST
firdaus
how many particles are in 2 moles of chromium
if so use the normal formula number of atom= number of particle/Avogadro's number
Aki
n= np/avogadtos constant. therefore n= 24/ 6.022×10²³
albert
24÷6.022×10²³
albert
@Albert is wrong
Aki
when you cross multiple it should give you Number of particles= mole*Avogadro's number X=2m*6.022*10^²³ X=1.20*10²⁴g
Aki
1.204×10^-22
Maame
please what is final velocity and initial velocity
don't know
Ekene
what do you want to become in future
Ekene
Nonso
I think initial velocity is the velocity that the mobile starts with at the start time (t=0s) but I don't think I heard abt final velocity
Malak
Malak where are you now I need to learn more from you
Ekene
initial velocity is the velocity an object possess at it intial position or is the starting velocity, while a final velocity is the velocity an object or body possess at it final stage or at the end of it motion
Mubarak
Bohr is kimia, of toksid, cloud, tree have cloud, tree, river but small from toksid fish or another.
Heavy, heavy kehidupan susah, kekayaan, berlambak, bergumpul. Dikenali.
Gravitional, Gravitional mean kehidup seseorang. Kehidupan bumi, kehidupan muka bumi, kehidupan dalam longitude, kehidupan dalam momentom, kehidupan dalam mongitude. Kehidupan dalam Pelajaran, mean Pelajar kolej.
firdaus
Nonconservative. Sains belajar
firdaus
hello
LFX
what are the types of kinetics
what is torque pls
An aluminum rod of length 1.8cm at 0°C is heated to produced a difference in length of 0.007cm. Calculate the temperature to which it is heated. Take the linear expansively aluminun as 2.3×10^-5 K^-1.
apply the formula... linear expansivity... everything you need are in the question already
Aki
Guys pls who understand equilibrium of forces mostly the calculation aspect
Faith
so can u explain how to solve the calculations
Faith
CcmT 0°0°M°T 4°4°0°0 4400°c Right Calculate 4400c Don't have rules with him
firdaus
please can someone explain how coulombs law is used to determine electric force
u know coulomb's law and electric force are related in a formula which is E=f/q where E is equals to electric field intensity and f is equals to the force while-q is equals to the charge
Juilet
and I guess no the formula for electric field intensity
Juilet
and I guess you know the formula for electric field intensity
Juilet
exactly what i want to say
Haruna
Field mean like don't have we give have.. Yap... That oil Airplan. Dshell n petrol..
firdaus
what is momentum
Momentum mean bacteria... OR CARE MONEY FROM STOLED.. OR CARE WE PLACE OR HOME FROM STOLED OR CARE WE BODY FROM STOLED
firdaus
Moment
firdaus
let him explain the statement well
Hello guys I'm new here
diewgatdet
hello
Godwin
Statement is resit, temu bual.
firdaus
the specimens of different materials can have same if their dimensions don't match a) resistance b) resistivity c) both d) statement is ambiguous
shoukat
b
diewgatdet
Bacteria.
firdaus
Specimen mean super human.. Power hin
firdaus
, yap like that lag
firdaus