What is Rotational inertia: Definition and 181 Discussions
The moment of inertia, otherwise known as the mass moment of inertia, angular mass, second moment of mass, or most accurately, rotational inertia, of a rigid body is a quantity that determines the torque needed for a desired angular acceleration about a rotational axis, akin to how mass determines the force needed for a desired acceleration. It depends on the body's mass distribution and the axis chosen, with larger moments requiring more torque to change the body's rate of rotation.
It is an extensive (additive) property: for a point mass the moment of inertia is simply the mass times the square of the perpendicular distance to the axis of rotation. The moment of inertia of a rigid composite system is the sum of the moments of inertia of its component subsystems (all taken about the same axis). Its simplest definition is the second moment of mass with respect to distance from an axis.
For bodies constrained to rotate in a plane, only their moment of inertia about an axis perpendicular to the plane, a scalar value, matters. For bodies free to rotate in three dimensions, their moments can be described by a symmetric 3 × 3 matrix, with a set of mutually perpendicular principal axes for which this matrix is diagonal and torques around the axes act independently of each other.
1. In the figure below, the pulley is a solid disk of mass M and radius R with rotational inertia .5MR. Two blocks, one of mass m1 and one of mass m2 hang from either side of the pulley by a light cord. Initially, the system is at rest with block 1 on the floor and block 2 at height h above...
Homework Statement
There are two uniform disks. Disk 1 has radius of R, a rotational inertia of I. Disk 2 has radius of 2R, what is the rotational inertia of Disk2 in term of I? The disks are rotating about their center axis.
Homework Equations
I = m * r ^ 2
Density = Mass / Area...
Homework Statement
You're holding a massless stick with a mass (m) on it at a distance (d) from your hand. You move the mass to 2d from your hand, how much larger force do you have to apply with your hand to keep the stick stable if the force you were applying before was F?Homework Equations...
Homework Statement
Doc Holliday takes his last shot of whiskey. His forearm and hand spans 18" and weighs 2lbs. The shotglass and its intoxicating contents weighs 5ozs. (there are 16 ozs in one pound). Doc remains otherwise motionless as his elbow bends, tossing back the whiskey.
Calculate...
Homework Statement
A pulley, with a rotational inertia of 2.0 10-3 kg·m2 about its axle and a radius of 20 cm, is acted on by a force applied tangentially at its rim. The force magnitude varies in time as F = 0.50t + 0.30t2, where F is in Newtons and t in seconds. The pulley is initially at...
Homework Statement
A bowling ball made for a child has two thirds the radius of an adult bowling ball. They are made of the same material (and therefore have the same mass per unit volume).
(a) By what factor is the mass of the child's ball reduced compared with the adult ball?
(b) By...
CORRECTION ON TITLE: it should be "Rotational Inertia Seesaw Pivot"Homework Statement
Alice (20kg) and Bonnie (25kg) sit on seesaw (10m long, 12 kg mass). Pivot of seesaw is in the middle. In order for the seesaw to stay level we determined (in the previous step of the multi-part problem)...
Hey everyone! I have a small problem with part b. I am wondering if i miscalculated something. Any ideas? Thanks!
Homework Statement
A 15 kg flywheel has all its mass around its outer rim. A string is wrapped around it and a m = 4.7 kg weight is hanging on the string. The flywheel...
Homework Statement
A pulley of moment of inertia I and radius r is fixed to a wall. A rope is wrapped around it and tied to a block of mass m. The block is initially held at rest, and then it is released. The block drops a distance h. The rope does not slip on the pulley, and the magnitude...
One expression for angular momentum is L=2m*(dA/dt),where m is the mass of the body in concern and (dA/dt) is the areal velocity of this rotating body.
What is the logical physical explanation (or description) for this?
Is there any other physical importance of this expression (or result)...
I need some help just getting moving on this problem...
A figure skater is spinning at a rate of 1.6 rev/s with her arms outstretched. She then draws her arms in toward her chest reducing her rotational inertia to 64% of its original value. What is her new rate of rotation??
I'm not sure...
Homework Statement
a. A merry go round is rotating in the counter-clockwise direction. Initially, a 50 kg child is sitting on the edge of the merry-go-around, which rotates at 0.5 radians per second. The moment of inertia of the merry-go-round is 2150 kg-m2. The radius is 2.50 meters. The...
I need to compute the energy to get a truck and trailer from 0 to 60 mph from rest taking into account the mass of truck and trailer and inertia of wheels and rims.
Do I treat the rims and tires as a cylindrical shell or solid cylinder? Once I find the energy of the tires and rims do I just...
Homework Statement
Two particles, each with mass m = 0.85 kg, are fastened to each other, and to a rotation axis at O, by two thin rods, each with length d = 5.6 cm and mass M = 1.2 kg. The combination rotates around the rotation axis with angular speed w = 0.30 rad/s. Measured about O, what...
Homework Statement
Three identical balls, with masses of M, 2M, and 3M, are fastened to a massless rod of length
L as shown. The rotational inertia about the left end of the rod is:
http://img13.imageshack.us/img13/1424/1234sjy.jpg
Homework Equations
I = MR^2
The Attempt at a Solution
I...
Homework Statement
The uniform solid block in Fig. 10-37 has mass .172 kg and edge lengths a = 0.035 m, b = .084 m, and c = .014 m. Calculate its rotational inertia about an axis through one corner and perpendicular to the large faces...
Homework Statement
A pulley, with a rotational inertia of 1.5 10-3 kg·m2 about its axle and a radius of 21 cm, is acted on by a force applied tangentially at its rim. The force magnitude varies in time as F = 0.50t + 0.30t^{2}, where F is in Newtons and t in seconds. The pulley is initially...
Rotational Inertia, Need Help With Integrals!
Homework Statement
In the figure below, a small disk of radius r = 2.00 cm has been glued to the edge of a larger disk of radius R = 4.00 cm so that the disks lie in the same plane. The disks can be rotated around a perpendicular axis through...
Homework Statement
In Fig. 10-43a, an irregularly shaped plastic plate with uniform thickness and density (mass per unit volume) is to be rotated around an axle that is perpendicular to the plate face and through point O. The rotational inertia of the plate about that axle is measured with the...
Homework Statement
A 103 g Frisbee is 16 cm in diameter and has about half its mass spread uniformly in a disk and the other half concentrated in the rim. With a quarter-turn flick of the wrist, a student sets the Frisbee rotating at 730 rpm.
a) What is the rotational inertia of the...
Homework Statement
A 120g Frisbee is 28cm in diameter and has about half its mass spread uniformly in a disk, and the other half concentrated in the rim. With a quarter-turn flick of the wrist, a student sets the Frisbee rotating at 560rpm.
(a) What is the rotational inertia of the...
How is rotational inertia effected by weight if at all? I am designing wheels and I'm considering the load placed on these wheels. I am not sure if the mass of the load should be incorperated into the inertia at all. Thanks!
Homework Statement
A rigid body is made of three identical thin rods, each with length L=0.600m, fastened together in the form of a letter H. The body is free to rotate about a horizontal axis that runs along the length of one of the legs of the H. The body is allowed to fall from rest from a...
1. Which rolls to the bottom of a hill sooner, a car tire alone or the same tire mounted on a rim?
a. The mounted tire, provided the tire is more massive than the rim
b. The tire alone, provided it is as heavy as the rim
c. The mounted tire, provided the tire is as heavy as the rim
d. The...
In the figure below, the pulley is a solid disk of mass M and radius R, with rotational inertia (MR2)/2. Two blocks, one of mass m1, and one of mass m2, hang from either side of the pulley by a light cord. Initially, the system is at rest, with Block 1 on the floor and Block 2 held at height h...
Homework Statement
A cylindrical rod 32.2 cm long has mass
0.919 kg and radius 1.54 cm. A 8.89 kg
ball of diameter 11.3 cm is attached to one
end. The arrangement is originally vertical
with the ball at the top and is free to pivot
about the other end.
The acceleration of gravity is 9.8 m/s2 ...
Homework Statement
Two particles, each with mass m=0.0036kg, are fastened to each other and to a rotation axis at P, by two thin rods, each with length L=0.68m and each with a mass of 0.0086kg. The combination rotates around the rotation axis with an angular velocity of 13.0rad/s. Find the...
Homework Statement
What is the rotational inertia of a solid iron disk of mass 46 kg, with a thickness of 6.31 cm and radius of 19.4 cm, about an axis through its center and perpendicular to it?
Homework Equations
either 1/2MR^(2) or I = sigma (1->N) Mi x Ri^(2)
The Attempt at a...
Thank you all for taking the time to help me out. Here's what I'm given:
Homework Statement
A solid door of mass M = 19 kg and width = 128 cm is hit at a right angle by a mud ball of mass m = 0.6 kg, which, as Fig. 10–44 shows, hits the door at the edge with speed v = 16 m/s and sticks...
hi guys I am having a problem with a physics problem.
the question is about a seesaw that has two masses, m_1 and m_2 at each end of the seesaw. the length of the seesaw is L, so each mass is a distance L/2 from the pivot (center). i answered the question for what the Inertia was for a...
A solid uniform sphere of radius R and mass M has a rotational inertia about a diameter that is given by (2/5)MR2. A light string of length 2R is attached to the surface and used to suspend the sphere from the ceiling. Its rotational inertia about the point of attachment at the ceiling is
-...
Homework Statement
What is the relationship between the inertia tensor and the rotational inertia? How can a second-rank tensor describe the same thing as a scalar? Is their a formula to go between one and the other i.e. if I have an inertia tensor for a rigid body rotating about some axis...
Homework Statement
A very light (meaning don't consider mass of the rod) rod is placed along the x axis. It has a mass m1=2.0kg at x=0, a mass m2=1.50kg at x=50cm, and a mass m3=3.0kg at x=100cm.
Find the moment of inertia of the system about a pivot point at x=0.Homework Equations...
Homework Statement
The pendulum consists of a uniform disk with radius r=10.0cm and mass 500g attached to a uniform rod with length L=500mm and mass 270g.
a. Calculate the rotational inertia of the pendulum about the pivot point.
(answer .205kg m^2)
b. What is the distance between the...
Rotational Inertia Problem--PLEASE HELP!
Homework Statement
Figure 12-39 shows a rigid structure consisting of a circular hoop, of radius R and mass m, and a square made of four thin bars, each of length R and mass m. The rigid structure rotates at a constant speed about a vertical axis...
[URGENT] Acceleration Problem due to Rotational Inertia [Exam in 9hrs!]
yes i know i might be late but i hope somebody can help me out with this problem because i can't figure it out. Exact word for word:
A block of mass m2= 12kg hangs from a rope. The rope wraps around a pulley and then...
1. Homework Statement :
In the figure, a stationary block explodes into two pieces L and R that slide across a frictionless floor and then into regions with friction, where they stop. Piece L, with a mass of 2.2 kg, encounters a coefficient of kinetic friction µL = 0.40 and slides to a stop in...
Homework Statement
A force of 21.09 N is applied tangentially to a wheel of radius 0.340 m and gives rise to an angular acceleration of 1.20 rad/s ^2. Calculate the rotational inertia of the wheel.
a) 7.46 kg . m2
b) 4.98 kg . m2
c) 8.96 kg . m2
d) 5.97 kg . m2
Homework Equations...
A 15.0-kg object is attached to a cord that is wrapped around a wheel of radius r = 9.0 cm (Fig. P8.60). The acceleration of the object down the frictionless incline is measured to be 2.00 m/s2. Assume the axle of the wheel to be frictionless.
(a) Determine the tension in the rope.
58.46681...
Homework Statement
A disk of radius R has an initial mass M. Then a hole of radius (1/4)R is drilled, with its edge at the disk center (The center of mass of the cutout is in the x positive direction). Find the new rotational inertia about the central axis.
Hint: Find the rotational...
In the figure below, a constant horizontal force Fapp of magnitude 17 N is applied to a wheel of mass 6 kg and radius 0.70 m. The wheel rolls smoothly on the horizontal surface, and the acceleration of its center of mass has magnitude 1.00 m/s2.
(a) In unit-vector notation, what is the...
A cockroach of mass m runs counterclockwise around the rim of a lazy Susan (a circular disc mounted on a vertical axle) of radius R and rotational inertia I with frictionless bearings. The cockroach's speed relative to the Earth is v, where as the lazy Susan turns clockwise with angular speed...
The masses and coordinates of four particles are indicated in the following table.
40 g x = 1.0 cm y = -4.0 cm
25 g x = 2.0 cm y = 4.0 cm
30 g x = -3.0 cm y = 5.0 cm
35 g x = 4.0 cm y = 4.0 cm
(a) What is the rotational inertia of this collection about the x axis?
g·cm2
(b) What is...
Hello everyone,
I'm having trouble with an application involving rotating a 10.8lb device through 60 degrees of rotation using a stepper motor (Hurst 4006-004: step angle .1 degrees, Output speed 3.33 rpm, rated torque at 175 pulses/sec of 162 oz-in). It appears that the motor is...
Homework Statement
A rigid structure consisting of a circular hoop of radius R and mass m, and a square made of four thin bars, each of length R and mass m. The rigid structure rotates at a constant speed about a vertical axis, with a period of rotation of 4.0 s. Assume R = 0.90 m and m = 3.0...
Homework Statement
i need to find the rotational inertia of a rod about a pivot. The rod is of mass M and length L and is attached to a pivot of negligible friction located at a distance of L/3 from the left end of the rod.
Homework Equations
The Attempt at a Solution
i know...
Homework Statement
There is a rectangular prism of uniform mass distribution with lengths of a, b, and c (b>a>c). Calculate it's rotational inertia about an axis through one corner and perpendicular to the large faces.Homework Equations
I = \int r^2 dm
r^2 = x^2 + y^2 + z^2
\rho =...
Homework Statement
A body radius R and mass m is rolling horizonttally without slipping with speed v. Then is rolls up a hill to maximum hieght h. If h=\frac{3v^2}{4g}
a) what is the body's rotational inertia?
b) What body might it be?
Homework Equations
h=\frac{3v^2}{4g}
The...
Homework Statement
A horizontal disc of diameter 10 cm is spinning freely about a vertical axis
through its centre at an angular speed of 80 revolutions per minute. A piece
of putty of mass 7.0 g drops on to and sticks to the disc a distance of 3.0 cm
from the centre. The angular speed...
Homework Statement
The rectangle shown has a mass, m. The sides are made of uniform thin wire. The short side is of length a, and the long side is of length b. If m = 5.50 g, a = 0.05 cm and b = 0.1 cm, what is the moment of rotational inertia about the axis indicated?
(ignore the x's)...