In this example we will apply the equations for constantangular acceleration to the simple case of a rotatingbicycle wheel. The angular velocity of the rear wheel of astationary exercise bike is wo = 4.00rad/s at timet = 0, and its angular acceleration is constant and equalto a = 2.15rad/s². A particular spoke coincides withthe + axis at time t = 0 (Figure 1). What angle doesthis spoke make with the + axis at time t = 3.00s?What is the wheel's angular velocity at this time?FigureAtt = 0:1 of 10o = 0 forchosen spokeSOLUTIONSET UP We take 0 = 0 at the postion where the chosen spoke is horizontal, and we take the counterclockwise rotation to be positive. Theinitial conditions are 0o = 0, wo = 4.00rad/s, and a = 2.15rad/s².SOLVE We can use the equations for constant angular acceleration to find and w at any time. The angle is given as a function of timeAlternatively,0Part A Practice Problem:The wheel has turned through three complete revolutions plus an additional 0.45 rev, or (0.45rev) (2π rad/rev) = 2.83rad = 162°.Thus, the chosen spoke is at an angle of 162° with the + axis.The wheel's angular velocity w is given as a fuction of time. At a time t = 3.00s,wo + at4.00rad/s+ (2.15rad/s²) (3.00s) = 10.5rad/sW====2wo² + 2a(0-00)(4.00rad/s)² + 2(2.15rad/s²) (21.7rad) = 109rad²/s²10.5rad/s = 1.66rev/sREFLECT Note the step-by-step similarity between these equations and the kinematic relationships for straight-line motion.=0o+wot+at²0+ (4.00rad/s) (3.00s) + (2.15rad/s²) (3.00s)²21.7rad = (21.7rad).1 rev2π rad= 3.45rev=How much longer will it take before the reference spoke is once again aligned with the + axis?Express your answer in seconds to three significant figures. Part B - Practice Problem:What will the angular speed of the wheel be at this time?Express your answer in radians per second to three significant figures.

Initial angular speed of real wheel ω0 =…

In this example we will apply the equations for constant angular acceleration to the simple case of a rotating bicycle wheel. The angular velocity of the rear wheel of a stationary exercise bike is wo = 4.00rad/s at time t = 0, and its angular acceleration is constant and equal to a = 2.15rad/s². A particular spoke coincides with the + axis at time t = 0 (Figure 1). What angle does this spoke make with the + axis at time t = 3.00s? What is the wheel's angular velocity at this time?

In this example we will apply the equations for constant angular acceleration to the simple case of a rotating bicycle wheel. The angular velocity of the rear wheel of a stationary exercise bike is wo = 4.00rad/s at time t = 0, and its angular acceleration is constant and equal to a = 2.15rad/s². A particular spoke coincides with the + axis at time t = 0 (Figure 1). What angle does this spoke make with the + axis at time t = 3.00s? What is the wheel's angular velocity at this time?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Angular speed, acceleration and displacement

Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.

Angular Position

Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.

Question

In this example we will apply the equations for constant
angular acceleration to the simple case of a rotating
bicycle wheel. The angular velocity of the rear wheel of a
stationary exercise bike is wo = 4.00rad/s at time
t = 0, and its angular acceleration is constant and equal
to a = 2.15rad/s². A particular spoke coincides with
the + axis at time t = 0 (Figure 1). What angle does
this spoke make with the + axis at time t = 3.00s?
What is the wheel's angular velocity at this time?
Figure
Att = 0:
1 of 1
0o = 0 for
chosen spoke
SOLUTION
SET UP We take 0 = 0 at the postion where the chosen spoke is horizontal, and we take the counterclockwise rotation to be positive. The
initial conditions are 0o = 0, wo = 4.00rad/s, and a = 2.15rad/s².
SOLVE We can use the equations for constant angular acceleration to find and w at any time. The angle is given as a function of time
Alternatively,
0
Part A Practice Problem:
The wheel has turned through three complete revolutions plus an additional 0.45 rev, or (0.45rev) (2π rad/rev) = 2.83rad = 162°.
Thus, the chosen spoke is at an angle of 162° with the + axis.
The wheel's angular velocity w is given as a fuction of time. At a time t = 3.00s,
wo + at
4.00rad/s+ (2.15rad/s²) (3.00s) = 10.5rad/s
W
=
=
=
=
2
wo² + 2a(0-00)
(4.00rad/s)² + 2(2.15rad/s²) (21.7rad) = 109rad²/s²
10.5rad/s = 1.66rev/s
REFLECT Note the step-by-step similarity between these equations and the kinematic relationships for straight-line motion.
=
0o+wot+at²
0+ (4.00rad/s) (3.00s) + (2.15rad/s²) (3.00s)²
21.7rad = (21.7rad).
1 rev
2π rad
= 3.45rev
=
How much longer will it take before the reference spoke is once again aligned with the + axis?
Express your answer in seconds to three significant figures.

Part B - Practice Problem:
What will the angular speed of the wheel be at this time?
Express your answer in radians per second to three significant figures.

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