*17—64.
If shaft BC is subjected to a torque of M = (0.4511/2)N -m,
where tis in seconds, determine the angular velocity of the
3-kg rod AB when t = 4 s, starting from rest. Neglect the
mass of shaft BC.
SOLUTION
Equations of Motion: The mass moment of
12—10.
The position of a particle along a straight line is given by
s = (1.5t3 — 13.5t2 + 2251‘) ft, where t is in seconds.
Determine the position of the particle whent = 6 s and the
total distance it travels during the 6-s time interval. Hint:
Plot the p
ABSOLUTE DEPENDENT MOTION ANALYSIS OF TWO
PARTICLES (Section 12.9)
Todays Objectives:
Students will be able to relate the
In-Class Activities:
positions, velocities, and
Check homework, if any
accelerations of particles
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undergoing dependent
CURVILINEAR MOTION: RECTANGULAR COMPONENTS
(Sections 12.4-12.5)
Todays Objectives:
Students will be able to:
a) Describe the motion of
a particle traveling
along a curved path.
b) Relate kinematic
quantities in terms of
the rectangular
components of the
v
RECTILINEAR KINEMATICS: ERRATIC MOTION
(Section 12.3)
Todays Objectives:
Students will be able to
determine position, velocity,
and acceleration of a particle
using graphs.
In-Class Activities:
Check homework, if any
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Applications
s-t, v-t
CURVILINEAR MOTION:
NORMAL AND TANGENTIAL COMPONENTS
(Section 12.7)
Todays Objectives:
Students will be able to
In-Class Activities:
determine the normal and
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tangential components of
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velocity and acceleration of a
Ap
INTRODUCTION & RECTILINEAR KINEMATICS:
CONTINUOUS MOTION (Sections 12.1 - 12.2)
Todays Objectives:
Students will be able to find
the kinematic quantities
(position, displacement,
velocity, and acceleration) of
a particle traveling along a
straight path.
I
RELATIVE MOTION ANALYSIS (Section 12.10)
Todays Objectives:
Students will be able to:
a) Understand translating
frames of reference.
b) Use translating frames of
reference to analyze
relative motion.
In-Class Activities:
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MOTION OF A PROJECTILE (Section 12.6)
Todays Objectives:
In-Class Activities:
Students will be able to
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analyze the free-flight motion of
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a projectile.
Applications
Kinematic equations for
projectile motion
Concept
12-118.
The truck travels in a circular path having a radius of 50 m at
a speed of v = 4 m/s. For a short distance from s = 0, its
speed is increased by 1') = (0.05s) m/sz, where s is in meters.
Determine its speed and the magnitude of its acceleration
wh
*16—4.
The disk is originally rotating at we = 8 rad/s. If it is (no = 8 rad/s
subjected to a constant angular acceleration of a = 6 rad/52, \
determine the magnitudes of the velocity and the n and t
components of acceleration of point B just after the wh
*17—4.
Determine the moment of inertia of the semiellipsoid with
respect to the x axis and express the result in terms of the
mass m of the semiellipsoid. The material has a constant
density p.
SOLUTION
_ yzdm
de — 2
Ans. 17—6.
Determine the mass moment
16—58.
If the block at C is moving downward at 4 ft /s, determine
the angular velocity of bar AB at the instant shown.
SOLUTION
Kinematic Diagram: Since link AB is rotating about fixed point A, then VB is always
directed perpendicular to link AB and its
16—111.
Crank AB rotates with the angular velocity and angular
acceleration shown. Determine the acceleration of the
slider block C at the instant shown.
SOLUTION
Angular Velocity: Since crank AB rotates about a fixed axis, Fig. a, oﬁ-m
’UB : (UAEVB = =
*14—8.
If the 50-kg crate is subjected to a force of P = 200 N, 1»-
determine its speed when it has traveled 15 m starting from
rest. The coefficient of kinetic friction between the crate
and the ground is ,uk = 0.3.
S O L U T | O N
Free-Body Diagram: Ref
12—51.
The a—t graph of the bullet train is shown. If the train starts
from rest, determine the elapsed time t’ before it again
comes to rest. What is the total distance traveled during this
time interval? Construct the v-t and s—t graphs.
SOLUTION
1) — t
13—14.
The 2-Mg truck is traveling at 15 m/s when the brakes on all its
wheels are applied, causing it to skid for a distance of 10 m
before coming to rest. Determine the constant horizontal force
developed in the coupling C, and the frictional force
deve
*15—64.
The three balls each have a mass m. If A has a speed I) just
before a direct collision with B, determine the speed of C
after collision. The coefficient of restitution between each
pair of balls e. Neglect the size of each ball.
SOLUTION
Conservat
15-6.
A train consists of a 50—Mg engine and three cars, each
having a mass of 30 Mg. If it takes 80 s for the train to
increase its speed uniformly to 40 km/h, starting from rest,
determine the force T developed at the coupling between
the engine E and t
PLANAR KINEMATICS OF A
RIGID BODY
RIGID
PLANAR KINEMATICS OF A RIGID BODY
There are cases where an object cannot be treated as a
particle. In these cases the size or shape of the body must be
considered. Also, rotation of the body about its center of
mass
CURVILINEAR MOTION: CYLINDRICAL COMPONENTS
(Section 12.8)
Todays Objectives:
In-Class Activities:
Students will be able to
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determine velocity and
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acceleration components
using cylindrical coordinates.
Applications
V