300 CHAPTER 10 ROTATIONAL KINEMATICS AND ENERGY The red spot of paint... is at the angular position 6. 10-1 Angular Positic To describe the motion of an ot Coordinate system with a defini nate system we can measure the Similarly, to describe rotat analogous to the linear positic which are defined in terms o Axle Reference line study of rotation. We begin b position. A FIGURE 10-1 Angular position The angular position, 0, of a spot of paint on a bicycle wheel. The reference line, where 0 = 0, is drawn horizontal here but any Angular Position, 0 Consider a bicycle wheel th say that the axle is the axi. every point on it moves in Now, suppose there is the rotational motion of direction can be chosen. the angle, 0, that a line cated in Figure 10-1.
300 CHAPTER 10 ROTATIONAL KINEMATICS AND ENERGY The red spot of paint... is at the angular position 6. 10-1 Angular Positic To describe the motion of an ot Coordinate system with a defini nate system we can measure the Similarly, to describe rotat analogous to the linear positic which are defined in terms o Axle Reference line study of rotation. We begin b position. A FIGURE 10-1 Angular position The angular position, 0, of a spot of paint on a bicycle wheel. The reference line, where 0 = 0, is drawn horizontal here but any Angular Position, 0 Consider a bicycle wheel th say that the axle is the axi. every point on it moves in Now, suppose there is the rotational motion of direction can be chosen. the angle, 0, that a line cated in Figure 10-1.
300 CHAPTER 10 ROTATIONAL KINEMATICS AND ENERGY The red spot of paint... is at the angular position 6. 10-1 Angular Positic To describe the motion of an ot Coordinate system with a defini nate system we can measure the Similarly, to describe rotat analogous to the linear positic which are defined in terms o Axle Reference line study of rotation. We begin b position. A FIGURE 10-1 Angular position The angular position, 0, of a spot of paint on a bicycle wheel. The reference line, where 0 = 0, is drawn horizontal here but any Angular Position, 0 Consider a bicycle wheel th say that the axle is the axi. every point on it moves in Now, suppose there is the rotational motion of direction can be chosen. the angle, 0, that a line cated in Figure 10-1.
If this bicycle wheel depicted makes 360 revolutions in 4 minutes and
48 seconds at constant speed, what was the average angular velocity of the wheel in units of radians per second?
(b)
If the diameter of the wheel is 27.5 inches, then what distance (arc length)
in meters has the red spot on the very outer periphery of the wheel travelled in 360 revolutions? (in meters)
(c)
How many meters has the red spot travelled in
just one revolution?
(d)
What is the Period of Rotation, T, (in units of seconds), of the red spot?
(e)
What is the tangential velocity of the red spot? (in units of
meters per second)?
(f)
The wheel is attached to a mountain bike that accelerates from a tangential linear speed of 4.47 m/s to 7.77 m/s in 21.8 seconds. What was the angular acceleration of the wheel during this acceleration period in units of rad/sec^2
?
Transcribed Image Text:300 CHAPTER 10 ROTATIONAL KINEMATICS AND ENERGY
The red spot of paint...
is at the
angular
position 6.
10-1 Angular Positic
To describe the motion of an ot
Coordinate system with a defini
nate system we can measure the
Similarly, to describe rotat
analogous to the linear positic
which are defined in terms o
Axle
Reference line
study of rotation. We begin b
position.
A FIGURE 10-1 Angular position The
angular position, 0, of a spot of paint on a
bicycle wheel. The reference line, where
0 = 0, is drawn horizontal here but any
Angular Position, 0
Consider a bicycle wheel th
say that the axle is the axi.
every point on it moves in
Now, suppose there is
the rotational motion of
direction can be chosen.
the angle, 0, that a line
cated in Figure 10-1.
Definition Definition Rate of change of angular velocity. Angular acceleration indicates how fast the angular velocity changes over time. It is a vector quantity and has both magnitude and direction. Magnitude is represented by the length of the vector and direction is represented by the right-hand thumb rule. An angular acceleration vector will be always perpendicular to the plane of rotation. Angular acceleration is generally denoted by the Greek letter α and its SI unit is rad/s 2 .
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