[pic] The flywheel of an engine has moment of inertia 2.5 kg•m2 about its rotation axis. What constant torque is required to bring it up to an angular speed of 400 rev/min in 8s, starting from at rest?

[pic] A solid, uniform cylinder with mass 8.25kg and diameter 15cm is spinning at 200 rpm on a thin, frictionless axle that stop the cylinder axis. You design a simple friction brake to stop the cylinder by pressing the brake against the outer rim with a normal force. The coefficient of kinetic friction between the brake and rim is 0.333. What must be the applied normal force to bring the cylinder to rest after it has turned through 5.25 rev?

[pic] A 2.2kg hoop 1.2m in diameter is rolling to the right without slipping on a horizontal floor at a steady 3 rad/s. (a) how fast is its center moving? (b) What is the total kinetic energy of the hip? (c) Find the velocity vector of each of the following points as viewed by a person at rest on the ground: i) the highest point on the hoop; ii) the lowest point on the hoop; iii) the point on the right side of the hoop, midway between the hoop and the bottom. (d) Find the velocity vector for each points in part c, except as viewed by someone moving along with same velocity as the hoop.

[pic] A solid ball is released from res and slides down a hillside that slopes downward at 65° from the horizontal. (a) What minimum value must the coefficient of static friction between the hill and ball surfaces have for no slipping to occur? (b) Would the coefficient of friction calculated in part a changed if the mass were doubled to 4kg?

[pic] A 392N wheel comes off a moving truck and rolls without slipping along a highway. At the bottom of a hill it is rotating at 25 rad/s. The radius of the wheel is 0.6m, and its moment of inertia about its axis is 0.8MR2. Friction does work on the wheel as it rolls up the hill to a stop, a height h above the bottom of the hill; this work has absolute value 3500J. Calculate h.

...Moment of inertia of a flywheel
Jonathan Prevett 13/11/14
Uday Ravish
Aim:
To determine the moment of inertia of a flywheel.
Apparatus:
Fly wheel and axel, weight hanger, slotted weights, stop watch, metre ruler.
Definitions:
Moment of Inertia- a quantity expressing a body's tendency to resist angular acceleration
Radius of Gyration- the distribution of the components of an object around an axis.
Method:
The weights were suspended from the axel by the cord, then we used a meter ruler to make sure it was 1m above the ground. The same person who is holding the weights has a stopwatch so they release the weights and start the stopwatch at the same time. They stop the stopwatch when the weights hit the floor. We repeated this for 4 different weights with both flywheels.
I=0.026 I=0.0095
Example Calculations:
Volume of section 1: L =
Angular Acceleration-
Radius of Gyration for axel: Torque=mgh
Moment of Inertia: +m2k2+m3k3
= 0.0245kgm²
For Aluminium,
Applications:
The very first known application of a flywheel is in a potter’s wheel to keep it spinning at a constant rate. Most promising as a direct alternative to chemical batteries in cases where uninterrupted direct current power is required. They have higher power...

...Moment of Inertia
1. Abstract
The goal of this study is to understand the transfer of potential energy to kinetic energy of rotation and kinetic energy of translation. The moment of inertia of the cross arm my group measured with the conservation of energy equation is: 0.01044 kg/m2 (with the mass of 15g), 0.01055 kg/m2 (with the mass of 30g), which is kind of similar to the standard magnitude of the moment ofinertia of the cross arm: 0.0095 kg/m2 (Gotten by measuring the radius and the mass of the cross arm and use the definition equation of momentinertia). And we also get the moment of inertia for disk: 0.00604 kg/m2, and the ring: 0.00494 kg/m2.
2. Introduction
For that experiment, we use the conservation of energy equation to find the moment of inertia of the cross arm, and then use the definition equation of the moment of inertia to get the exact magnitude for the cross arm, the disk and the ring.
For the first step, finding the moment of inertia of cross arm, we need the conservation of energy equation for the transferring of the energy from the potential energy to the sum of the kinetic energy for both the mass strikes and the cross arm, like equation 1:
Since the mass is falling with uniform acceleration, its final velocity,...

...Moment of Inertia Formula
The Moment of inertia is the property by the virtue of which the body resists angular acceleration. In simple words we can say it is the measure of the amount of moment given to the body to overcome its own inertia.
It’s all about the body offering resistance to speed up or slow down its own motion.
Moment of inertia is given by the formula
Where
R = Distance between the axis and rotation in m
M = Mass of the object in Kg.
Hence the Moment of Inertia is given in Kgm2.
Moment of Inertia Formula helps to calculate the moment of inertia of the given body. It depends on the shape and mass distribution of the body and on the orientation of the rotational axis.
Moment of Inertia Problems
Below are given problems based on moment of inertia which helps you to understand where we can use these formulas.
Question 1: Calculate the Moment of inertia of the ball having mass of 5 Kg and radius of 3 cm?
Solution:
Given: Mass of the ball = 5Kg,
Radius of the ball = 3 cm = 0.03 m,
Moment of Inertia is given by I = MR2
= 5 Kg × (0.03 m)2
= 0.0045...

...MOMENT OF INERTIA
Chua, Richard Janssen J., PHY11L/A3
chardsenchua77@yahoo.com
Abstract
The moment of inertia, or also known as the rotational inertia, is the rotational analog of a rigid body to a linear or an angular motion. It is one of the fundamentals of the dynamics of rotational motion. The moment of inertia must always be in a specified chosen axis of rotation. The point of motion is basically defined as the relationship between mass and the perpendicular distance to the rotational axis.
KEYWORDS: Moment of Inertia, Rigid body, Angular motion, Axis of rotation
Introduction
Moment of inertia is always defined with respect to a specific axis of rotation. The mass moment of inertia with respect to an axis is also defined as the product of the mass times the distance from the axis squared.
(1)
The moment of inertia of any extended object or rather a continuous mass is built up from the same basic principle.
(2)
The general form of the moment of inertia involves an integration of the mass relative to the axis of rotation.
(3)
Density is mass per unit volume,, where the density of the body is uniform.
(4)
Fig. 1: Hollow...

...Title: Mass Moment of Inertia
Objective:
To determine mass moment of inertia of a part using experimental method.
Theory:
If a part has been designed and built, its mass moment of inertia can be determined approximately by a simple experiment. This requires that the part be swung about any axis (other than one that passes through its CG) parallel to that about which the moment is sought and its period of pendular oscillation measured. Figure 1 shows a part of connecting rod suspended on a knife-edge pivot at ZZ and rotated through a small angle θ.
Its weight force W acts as its CG has a component W sin θ perpendicular to the radius r from the pivot to the CG.
From rotational form of Newton’s equation:
TZZ=IZZ∝
Substituting equivalent expressions for TZZ and ∝;
-Wsin θr=IZZd2θdt2
Where the negative sign is used because the torque is in the opposite direction to angle a.
For small values of θ, sinθ=θ, approximately, so:
-Wθr=IZZd2θdt2
d2θdt2=-WrIZZθ
Equation above is a second order differential equation with constant coefficients that has the well-known solution:
θ=CsinWrIZZt+DcosWrIZZt
The constants of integration C and D can be found from the initial conditions defined at the instant the part of released and allowed to swing.
At: t=0, θ=θmax, ω=dθdt=0;then:C=0, D=θmax
And:
θ=θmaxcosWrIZZt
Equation above defines the part’s motion as a cosine wave that...

...Moment of Inertia
Academic Resource Center
What is a Moment of Inertia?
• It is a measure of an object’s resistance to changes to its
rotation.
• Also defined as the capacity of a cross-section to resist
bending.
• It must be specified with respect to a chosen axis of rotation.
• It is usually quantified in m4 or kgm2
Quick Note about Centroids….
• The centroid, or center of gravity, of any object is the point
within that object from which the force of gravity appears to
act.
• An object will remain at rest if it is balanced on any point
along a vertical line passing through its center of gravity.
and more…
• The centroid of a 2D surface is a point that corresponds to the
center of gravity of a very thin homogeneous plate of the
same area and shape.
• If the area (or section or body) has one line of symmetry, the
centroid will lie somewhere along the line of symmetry.
Perpendicular Axis Theorem
• The moment of inertia (MI) of a plane area about an axis
normal to the plane is equal to the sum of the moments of
inertia about any two mutually perpendicular axes lying in the
plane and passing through the given axis.
• That means the Moment of Inertia Iz = Ix+Iy
Parallel Axis Theorem
• The moment of area of an object about
any axis parallel to the centroidal axis is
the sum of MI...

...AP Physics Summer Assignment with
Dr. Crymes
Welcome to AP Physics B! It is a college level
physics course that is fun, interesting, and challenging
on a level you’ve not yet experienced. This assignment
will review all of the prerequisite knowledge expected of
you. There are 7 parts to this assignment. By taking the
time to review and understand all parts of this
assignment, you will help yourself acclimate to the rigor
and pacing of APPhysics. The summer assignment will
be “due” the first day of class. Good luck!
1. First off: send me your email address to jonathan_crymes@gwinnett.k12.ga.us so that I can make a class
list and hopefully send you some cool stuff over the summer. No extra work, I promise. Preferably
today, but no later than June 30, email me to introduce yourself. Please include the following
information with your email:
- First name, last name, last math class taken and grade received.
- What do you hope to get out of this course besides a good grade?
- Do you have any physicsquestions you’ve always wondered about like: what is a black hole? Is time
travel really possible? What is “relativity”? or “quantum physics”? or “if the Universe is filled with
stars, why is it dark in space but not on Earth?” or the classic “Did Einstein really fail his math class?”
2. Okay, remember how in chemistry they use symbols like “O” for oxygen and “H” for...

...Sadie D. Hood Lab 8: Moment of Inertia Partner: Florence Doval Due 16 November 2011 Aims: To use a centripetal force apparatus to calculate the moment of inertia of rotating weights, using theories derived from ideas of energy transfer (Im = MR2 (g/2h)(t2-t02)) and point mass appoximation (m1r12 + m2r22). Set Up
Procedure First we measured the weights of two masses and wingnuts that secure them. Then we placed one of the masses on the very end of a horizontal rod on the centripetal force apparatus, 0.162 m away from the centre of the rod, and the other mass 0.115 m away from the centre of the rod. Then we attached a 0.2 kg mass to the bottom of a string and wound the string around the vertical shaft of the apparatus, so that the bottom of the weight rose to the bottom edge of the tabletop the apparatus was on. We measured the distance from the bottom of the weight to the floor, and then let the weight fall to the floor, and measured the time it took to do so. We repeated this measurement, using the same initial height, four more times. Then we took the masses and the wingnuts off the horizontal rod and let the 0.2 kg mass fall in the same way as before, five times. Then we replaced the masses and the wingnuts, but put them both on the edges of the horizontal rod, and repeated the same falling mass measurements five times. We moved the masses in towards the centre of the rod and continued to repeat the falling mass...

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