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?

University Physics Volume 1

18th Edition

ISBN:9781938168277

Author:William Moebs, Samuel J. Ling, Jeff Sanny

Publisher:William Moebs, Samuel J. Ling, Jeff Sanny

Chapter10: Fixed-axis Rotation

Section: Chapter Questions

Problem 10.2CYU: Check Your Understanding A centrifuge used in DNA extraction spins at a maximum rate of 7000 rpm,...

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