PHYS 1001 - Fall 2012: Problem Set 8
due in class Monday Nov. 26 2012
All questions are worth 5 points.
1. A wheel of radius 24.6 cm whose axis is xed starts form rest and reaches an angular velocity of 4.15
rad/s in 2.68 s due to a force of 13.4 N acting
PHYS 1001 - Fall 2012: Tutorial 4
1. A spider is suspended from a single vertical thread; the spider has mass m = 30 mg. The spider is
acted upon by the force of gravity, which is directed downward and has magnitude 3.0 104 N, and
by the tension T in the
PHYS 1001 - Fall 2012: Problem Set 7
due in class Monday Nov. 19 2012
All questions are worth 5 points.
1. An air puck with mass 0.15 kg and velocity (1.7m/s) (2.0m/s) on a frictionless table collides
i
j
(Fig. 8-39 on page 243 of the textbook).
with a s
PHYS 1001 - Fall 2012: Tutorial 3
1. A melon is dropped from height 58.3 m. At the same moment somebody on the ground straight below
the melon(height 0 m) shoots an arrow up with initial velocity 25.1 m/s.
(a) How long after the melon is dropped will the
PHYS 1001 - Fall 2012: Problem Set 6
due in class Monday Nov. 12 2012
All questions are worth 5 points.
1. A block is constrained to move without friction along the x-axis. The block is attached to a spring of
equilibrium length L. The other end of the sp
PHYS 1001 - Fall 2012: Problem Set 9
due in class Monday Dec. 3 2012
1. What is the angular momentum about the origin of a particle of mass 270 g at position r = (0.1
i
0.5 + 0.2k)m, moving with a velocity of v = (12 7 3k)m/s?
j
i
j
[3]
2. A rock of mass
PHYS 1001 - Fall 2012: Tutorial 1
1. A skydiver jump from an airplane at 3000 m. After a certain time the skydiver will attain a so-called
terminal velocity, which is the maximal velocity that he will reach. This terminal velocity depends on
the accelerat
PHYS 1001 - Fall 2012: Tutorial 2
= 2 + 1
a) Draw this vector with its origin at the intersection of the x and y axis. What angle does it
make
with the x axis?
b) Draw a vector u orthogonal to . W hat are the components of u? Verify that
+ = 0.
1. Consi
PHYS 1001 - Fall 2012: Tutorial 5
Week of October 22.
1. Consider the three-pulley arrangement shown below. The three masses m1 , m2 and m3 have the values 4.00, 10.00 and 6.00 kg, respectively. All the pulleys are frictionless and the strings are massles
PHYS 1001 - Fall 2012: Tutorial 6
Week of November 5.
1. Two blocks of masses m1 = 5 kg and m2 = 3 kg are linked by a rope of negligible mass that goes
through two frictionless and massless pulleys. The smaller of the two masses is attached to a spring of
PHYS 1001 - Fall 2012: Tutorial 7
Week of November 12 2012.
1. Find the location of the center of mass for a one-dimensional rod of length L and of linear density
(x) = cx, where c is a constant. (Hint: You will need to calculate the mass in terms of c an
Chapter 2: Straight-Line (1D) Motion
Physics 1301: Chapter 2, Pg 1
Main concepts
Physics 1301: Chapter 2, Pg 2
Position and displacement
r (t ) x(t ) y (t ) z (t )
y
z
0
r (t )
x(t )
r (t )
x(t ) y (t ) z (t )
y
z
0
r (t )
x(t )
Physics 1301: Chapter 2, P
Chapter 4: Newtons Laws Forces Inertial reference frames Newton's first law inertia Newtons second law F = ma Newtons third law action-reaction forces Identifying forces; free-body diagrams
Physics 1301: Chapter 4, Pg 1
Forces Kinematics relates position
Angular momentum: point mass Point mass:
L = rp
L = rp sin = r p = rp
Angular momentum is analogous to linear momentum Does constant momentum implies constant angular momentum? Yes! Does constant angular momentum implies constant momentum? No!
System:
L =
Vectors
B or B
|B| B
Physics 1301: Chapter 1, Pg 24
Displacement vector
Physics 1301: Chapter 1, Pg 25
Vector algebra: vector addition
A B
B A
Physics 1301: Chapter 1, Pg 26
Sum of three vectors: Associativity
( A B) C
A (B C)
Physics 1301: Chapter 1, Pg
Chapter 3: Motion in 2D and 3D
Position and displacement Velocity and speed Acceleration Trajectories Motion with constant acceleration Projectile motion Uniform circular motion Relative motion
Physics 1301: Chapter 2, Pg 1
Position vector Position vector
Chapters 9 & 10: Rotations of Rigid Bodies
Rotation of a rigid body angular displacement, angular velocity, angular acceleration Rotational inertia and Rotational kinetic energy Torque, Newtons second law for rotations, Angular momentum and its conservati
Chapter 5: Application of Newtons Laws Force of gravity, weight Tension Normal force Force of friction Spring force Drag force Uniform circular motion
Physics 1301: Chapter 5, Pg 1
Force of gravity Experiment:
All free objects (regardless of mass) acceler
Chapter 6: Work and Kinetic Energy Kinetic Energy Work Power Work of some common forces Net work Work Kinetic Energy theorem Path dependence of work Conservative and non-conservative Forces, central forces
Physics 1301: Chapter 6, Pg 1
Conservation laws
N
Chapter 7: Potential energy and conservation of Energy
Potential energy Conservation of energy Using conservation of energy to find motion Allowed motion Relation between force and potential energy
Physics 1301: Chapter 7, Pg 1
Potential energy and work o
Chapter 8: Linear momentum, collisions, and CM
Systems of particles: internal and external forces Momentum and its conservation Impulse Inelastic and elastic collisions Center of mass (CM) Collisions in CM reference frame
Physics 1301: Chapter 8, Pg 1
Mom
Statics Statics studies rigid motionless objects
Used in structural engineering and design
Dynamical equations for rigid body
dp = Fnet (1.a ) dt
dL = net (1.b) dt
Motion of the rigid object is governed by external forces and torques!
If object is not mov
Simple harmonic motion
Equation of motion: Trial solution:
d 2x d 2x m 2 = kx +2x = 0 dt dt 2
x = Bet
dx d 2x = Bet = x; = B 2et = 2 x dt dt 2
Note: x is real, but B and can be complex!
d Derivatives: ~ dt
Equation for :
2 x + 2 x = 0 2 = 2 1, 2 = i
Gene
Oscillatory motion Kinematics and properties of simple harmonic motion Relationship among position, velocity, and acceleration Connection to circular motion Springs Energy Pendulums, simple and physical Damped and driven harmonic motion
Simple harmonic mo
Dot product of two vectors Definition 1:
A B = AB cos
Properties: AB = BA
A (B + C) = A B + A C
Parallel and orthogonal vectors:
A | B cos = 1 A B = AB A B cos = 0 A B = 0
Dot product of a vector with itself:
A A = A2
Physics 1301: Chapter 6, Pg 6
Dot pr
Cross (vector) product of two vectors
Cross product:
A B = C C = AB sin ; C A; C B
Properties: A B = B A
A (B + C) = A B + A C
Parallel and orthogonal vectors:
A | B sin = 0 A B = 0 A B sin = 1 A B = AB
Cross product of a vector with itself:
AA = 0
Mixed