8/11/2019 Rotational Motion of Solid Objects 8.1-8.3 http://slidepdf.com/reader/full/rotational-motion-of-solid-objects-81-83 1/46 Announcements Review Quantities in Rotational Motion Center of Mass Torque Final Questions Chapter 8 Rotational Motion of Solid Objects Rotational Motion of Solid Objects
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8/11/2019 Rotational Motion of Solid Objects 8.1-8.3
Announcements Review Quantities in Rotational Motion Center of Mass Torque Final Questions
Physics Concept: Energy
Energy (scalar): The ability to do work. Energy is a physical quantity that can be measured, though its value
depends upon the inertial frame of reference (SI units: joules; 1 J = 1 N · m = 1 kg · m2/s2).
The Conservation of Energy
Energy can be neither created nor destroyed, it can only be changed from one form to another or transferred fromone body to another. The total amount of energy is always the same.
Types of energy
Kinetic energy: the energy an object possesses due to its motion
K =1
2mv
2
Potential energy: the energy stored in the forces between or within objects.
Gravitational potential energy: the energy stored in the gravitational forces between an object andthe Earth
U g = mgh
Elastic potential energy: the energy in the forces within a distorted elastic object
Announcements Review Quantities in Rotational Motion Center of Mass Torque Final Questions
Scenario
During spring semester at MIT, residents of the parallel buildings of the East Campus dorms battle one anotherwith large catapults that are made with surgical hose mounted on a window frame. A 0.5 kg balloon filled withdyed water is placed in a pouch attached to the hose, which is then stretched through the width of the room.Assume that the stretching of the hose obeys Hooke’s law and has a spring constant of 100 N/m.
Announcements Review Quantities in Rotational Motion Center of Mass Torque Final Questions
Scenario
During spring semester at MIT, residents of the parallel buildings of the East Campus dorms battle one anotherwith large catapults that are made with surgical hose mounted on a window frame. A 0.5 kg balloon filled withdyed water is placed in a pouch attached to the hose, which is then stretched through the width of the room.Assume that the stretching of the hose obeys Hooke’s law and has a spring constant of 100 N/m.
Question
Assume that the hose is stretched by 5.00 m and then released. What is the speed of the balloon in the pouchwhen the hose reaches its relaxed length?
Announcements Review Quantities in Rotational Motion Center of Mass Torque Final Questions
Scenario
During spring semester at MIT, residents of the parallel buildings of the East Campus dorms battle one anotherwith large catapults that are made with surgical hose mounted on a window frame. A 0.5 kg balloon filled withdyed water is placed in a pouch attached to the hose, which is then stretched through the width of the room.Assume that the stretching of the hose obeys Hooke’s law and has a spring constant of 100 N/m.
Question
Assume that the hose is stretched by 5.00 m and then released. What is the speed of the balloon in the pouchwhen the hose reaches its relaxed length?
Answer
To answer this question, we will use conservation of energy
Announcements Review Quantities in Rotational Motion Center of Mass Torque Final Questions
Scenario
During spring semester at MIT, residents of the parallel buildings of the East Campus dorms battle one anotherwith large catapults that are made with surgical hose mounted on a window frame. A 0.5 kg balloon filled withdyed water is placed in a pouch attached to the hose, which is then stretched through the width of the room.Assume that the stretching of the hose obeys Hooke’s law and has a spring constant of 100 N/m.
Question
Assume that the hose is stretched by 5.00 m and then released. What is the speed of the balloon in the pouchwhen the hose reaches its relaxed length?
Answer
To answer this question, we will use conservation of energy
When the hose is stretched, the energy of the system is all in the form of elastic potential energy
E i = 12 kx
2
Rotational Motion of Solid Objects
A t R i Q titi i R t ti l M ti C t f M T Fi l Q ti
Announcements Review Quantities in Rotational Motion Center of Mass Torque Final Questions
Scenario
During spring semester at MIT, residents of the parallel buildings of the East Campus dorms battle one anotherwith large catapults that are made with surgical hose mounted on a window frame. A 0.5 kg balloon filled withdyed water is placed in a pouch attached to the hose, which is then stretched through the width of the room.Assume that the stretching of the hose obeys Hooke’s law and has a spring constant of 100 N/m.
Question
Assume that the hose is stretched by 5.00 m and then released. What is the speed of the balloon in the pouchwhen the hose reaches its relaxed length?
Answer
To answer this question, we will use conservation of energy
When the hose is stretched, the energy of the system is all in the form of elastic potential energy
E i = 12 kx
2
When the hose reaches its relaxed length, the energy of the system is all in the form of kinetic energy of
the balloon E f = 12 mv
2
Rotational Motion of Solid Objects
Announcements Review Quantities in Rotational Motion Center of Mass Torque Final Questions
Announcements Review Quantities in Rotational Motion Center of Mass Torque Final Questions
Scenario
During spring semester at MIT, residents of the parallel buildings of the East Campus dorms battle one anotherwith large catapults that are made with surgical hose mounted on a window frame. A 0.5 kg balloon filled withdyed water is placed in a pouch attached to the hose, which is then stretched through the width of the room.
Assume that the stretching of the hose obeys Hooke’s law and has a spring constant of 100 N/m.
Question
Assume that the hose is stretched by 5.00 m and then released. What is the speed of the balloon in the pouchwhen the hose reaches its relaxed length?
Answer
To answer this question, we will use conservation of energy
When the hose is stretched, the energy of the system is all in the form of elastic potential energy
E i = 12 kx
2
When the hose reaches its relaxed length, the energy of the system is all in the form of kinetic energy of
the balloon E f = 12 mv
2
By conservation of energy, E i = E f ; solving for v :
v =
kx 2
m
1/2
=
(100 N/m)(5.00 m)2
0.5 kg
1/2
= 70.7 m/s
Rotational Motion of Solid Objects
Announcements Review Quantities in Rotational Motion Center of Mass Torque Final Questions
Translational motion is the motion of an object from one place to another (what we have discussed so far)
Rotational motion
Rotational motion is the motion of an object around a point
Newton’s First Law (Law of Inertia)
“An object will stay at rest or continue at a constant velocity unless acted upon by an external unbalanced force”
Newton’s First Law of Rotational Motion (Law of Rotational Inertia)“A rigid object (that is not wobbling) will stay at rest or continue rotating at a constant angular velocity unlessacted upon by an external unbalanced torque”
A body at rest tends to remain at rest
A body that’s rotating tends to remain rotating
Rotational Motion of Solid Objects
Announcements Review Quantities in Rotational Motion Center of Mass Torque Final Questions
Translational motion is the motion of an object from one place to another (what we have discussed so far)
Rotational motion
Rotational motion is the motion of an object around a point
Newton’s First Law (Law of Inertia)
“An object will stay at rest or continue at a constant velocity unless acted upon by an external unbalanced force”
Newton’s First Law of Rotational Motion (Law of Rotational Inertia)“A rigid object (that is not wobbling) will stay at rest or continue rotating at a constant angular velocity unlessacted upon by an external unbalanced torque”
A body at rest tends to remain at rest
A body that’s rotating tends to remain rotating
Physics Concept: Rotational inertia
Rotational inertia: the resistance of an object to a change in its rotation
Physics Concept: Rotational mass
Rotational mass (moment of inertia): the measure of an object’s rotational inertia
Rotational Motion of Solid Objects
Announcements Review Quantities in Rotational Motion Center of Mass Torque Final Questions
In 1974, Frenchman Philippe Petit, walked (and danced) on a cable suspended between the World Trade Centertowers. He carried with him a custom-made 8.0 m pole. Why?
Rotational Motion of Solid Objects
Announcements Review Quantities in Rotational Motion Center of Mass Torque Final Questions
In 1974, Frenchman Philippe Petit, walked (and danced) on a cable suspended between the World Trade Centertowers. He carried with him a custom-made 8.0 m pole. Why?
AnswerThe pole increased his rotational inertia, thereby increasing his resistance to rotate (which would cause him to fall)
The center of mass of an object is the point about which an object’s mass balances
Properties of the center of mass
An object behaves as if all of its mass is at its center of mass (we can imagine that the gravitational forceis only acting at the object’s center of mass)
A freely rotating object (one without a fixed axis) rotates about its center of mass
Rotational Motion of Solid Objects
Announcements Review Quantities in Rotational Motion Center of Mass Torque Final Questions
The center of mass of an object is the point about which an object’s mass balances
Properties of the center of mass
An object behaves as if all of its mass is at its center of mass (we can imagine that the gravitational forceis only acting at the object’s center of mass)
A freely rotating object (one without a fixed axis) rotates about its center of mass
In the 1968 Olympics, Dick Fosbury introduced a new style of jumping to the high-jump event and won the goldmedal. Why is the peculiar form of the so-called Fosbury advantageous?
Answer
It lowers the altitude of the center of mass of the athlete
Rotational Motion of Solid Objects
Announcements Review Quantities in Rotational Motion Center of Mass Torque Final Questions
“An object will stay at rest or continue at a constant velocity unless acted upon by an external unbalanced force.”
Newton’s First Law of Rotational Motion (Law of Rotational Inertia)“A rigid object (that is not wobbling) will stay are rest or continue rotating at a constant angular velocity unlessacted upon by an external unbalanced torque.”
A body at rest tends to remain at rest
A body that’s rotating tends to continue rotating
Newton’s Second Law of Motion
“The net force on an object is equal to the mass m of the object multiplied by its acceleration −→a . Theacceleration is in the same direction as the net force.”
−→
F = m−→a
Newton’s Second Law of Rotational Motion
“The net torque on an object (that is not wobbling) is equal to the rotational mass I of the object multiplied by itsangular acceleration −→α . The angular acceleration is in the same direction as the net torque.”
−→τ = I −→α
Rotational Motion of Solid Objects
Announcements Review Quantities in Rotational Motion Center of Mass Torque Final Questions
To get something to start spinning, we must apply atorque
To apply a torque we need
a pivot pointa lever arman applied force
The magnitude of the torque = lever arm · forceperpendicular to lever arm
τ = r · F ⊥
The direction of the torque is given by the right-handrule:
point your right hand in the direction of thelever armcurl your fingers in the direction of the appliedforceThe direction of your outstretched thumb is the
Two mechanics are using wrenches to loosen screws on a ship. One of the mechanics is rather wimpy and can onlyexert half the force that the other mechanic can in turning a wrench. Though weak, he is very crafty and hasdevised a custom wrench for himself that is 1 m long (the other mechanic’s wrench is only 0.5 m long). Assumingboth mechanics have perfect “wrench form”, which mechanic has an easier time loosening screws?
Rotational Motion of Solid Objects
Announcements Review Quantities in Rotational Motion Center of Mass Torque Final Questions
Two mechanics are using wrenches to loosen screws on a ship. One of the mechanics is rather wimpy and can onlyexert half the force that the other mechanic can in turning a wrench. Though weak, he is very crafty and hasdevised a custom wrench for himself that is 1 m long (the other mechanic’s wrench is only 0.5 m long). Assumingboth mechanics have perfect “wrench form”, which mechanic has an easier time loosening screws?
AnswerThey are both equally as easy
Rotational Motion of Solid Objects
Announcements Review Quantities in Rotational Motion Center of Mass Torque Final Questions