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12 Chaptert Doing Physics
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Problem Solving Circular Motion Dynamics
Challenge Problems
Problem 1: Double Star System
Consider a double star system under the influence of gravitational force between the
stars. Star 1 has mass m1
Module 10: Circular Motion Dynamics
10.1 Newtons Second Law and Circular Motion
We have already shown that when an object moves in a circular orbit of radius R with
angular velocity ! , it is most con
Central Force Motion
Central Force Problem
Find the motion of two bodies interacting via a central force.
Examples:
Gravitational force (Kepler problem):
r
m1m2
F1,2 (r ) = !G 2 r
r
Linear restoring f
Kepler Problem
Concept Questions
Question1 Which of the following are Keplers Laws?
A. Each planet moves in an elliptical orbit, with the sun at the center of the ellipse.
B. Each planet moves in an
Kepler Problem
Concept Questions
Question1 Which of the following are Keplers Laws?
A. Each planet moves in an elliptical orbit, with the sun at the center of the ellipse.
B. Each planet moves in an
Central Force Motion
Challenge Problems
Problem 1: Elliptic Orbit
A satellite of mass ms is in an elliptical orbit around a planet of mass m p which is
located at one focus of the ellipse. The satelli
Central Force Motion
Challenge Problems
Problem 1: Elliptic Orbit
A satellite of mass ms is in an elliptical orbit around a planet of mass m p which is
located at one focus of the ellipse. The satelli
Module 28: The Kepler Problem: Planetary Mechanics
28.1 Introduction Keplers Laws:1
1. Each planet moves in an ellipse with the sun at one focus.
2. The radius vector from the sun to a planet sweeps
Problem Solving Circular Motion Dynamics
Problem 1: Double Star System
Consider a double star system under the influence of gravitational force between the
stars. Star 1 has mass m1 and star 2 has mas
Circular Motion Dynamics
Concept Questions
Problem 1: A puck of mass m is moving in a circle at constant speed on a frictionless
table as shown above. The puck is connected by a string to a suspended
Circular Motion Dynamics
Concept Questions
Problem 1: A puck of mass m is moving in a circle at constant speed on a frictionless
table as shown above. The puck is connected by a string to a suspended
UMass Boston
Fundamentals of Physics I
Summer Morning Session
Prof. Tomas Materdey, Office: S-3-110; Phone: (617) 287-6435, e-mail: tomas.materdey[email protected]
1. Registration: All students are required to
Circular Motion
8.01
Position and Displacement
r
r (t ) : position vector
o f a n o b je c t m o v in g in a
circular orbit of radius R
r
!r (t ): change in position between time t and
time t+t
P o s
Circular Motion
Concept Questions
Question 1 A bead is given a small push at the top of a hoop (position A) and is
constrained to slide around a frictionless circular wire (in a vertical plane). Circl
Circular Motion
Concept Questions
Question 1 A bead is given a small push at the top of a hoop (position A) and is
constrained to slide around a frictionless circular wire (in a vertical plane). Circl
Problem Solving Circular Motion Kinematics
Challenge Problem Solutions
Problem 1
A bead is given a small push at the top of a hoop (position A) and is constrained to slide
around a frictionless circul
Problem Solving Circular Motion Kinematics
Challenge Problems
Problem 1
A bead is given a small push at the top of a hoop (position A) and is constrained to slide
around a frictionless circular wire (
Chapter 9 Uniform Circular Motion
9.1 Introduction
Special cases often dominate our study of physics, and circular motion is certainly no
exception. We see circular motion in many instances in the wor
Cartesian Coordinate System
and Vectors
Coordinate System
Coordinate system: used to describe the position
of a point in space and consists of
1. An origin as the
reference point
2. A set of coordin
Vectors
Concept Questions
Question 1. Consider the pair of units vectors ( P , P ) located at the point P , and the
ij
pair of units vectors ( , ) located at the point S . Which of the following state
Vectors
Concept Questions
Question 1. Consider the pair of units vectors ( P , P ) located at the point P , and the
ij
pair of units vectors ( , ) located at the point S . Which of the following state
Conservation of Energy
Concept Questions
Question 1: A block of inertia m is attached to a relaxed spring on an inclined plane. The
block is allowed to slide down the incline, and comes to rest. The c
Conservation of Energy
Challenge Problem Solutions
.
Problem 1
An object of mass m is released from rest at a height h above the surface of a table. The
object slides along the inside of the loop-the-
Conservation of Energy
Challenge Problems
Problem 1
An object of mass m is released from rest at a height h above the surface of a table. The
object slides along the inside of the loop-the-loop track
Module 14: Application of the Principle of Conservation of
Energy
In the preceding chapter we consider closed systems !Esystem = 0 in which the only
interactions on the constituents of a system were d
Two-Dimensional Rotational
Kinematics: Angular
Momentum
Review: Cross Product
Magnitude: equal to the area of the parallelogram defined by
the two vectors
)(
)
rr
rr
rr
r
r
A # B = A B sin ! = A B sin
Angular Momentum
Concept Questions
Question 1: Angular Momentum
In the above situation where a particle is moving in the x-y plane with a constant velocity, the
!
magnitude of the angular momentum L 0
Angular Momentum
Concept Questions
Question 1: Angular Momentum
In the above situation where a particle is moving in the x-y plane with a constant velocity, the
!
magnitude of the angular momentum L 0