Skip to main content
Ch 09: Rotation of Rigid Bodies
Young & Freedman Calc - University Physics 15th Edition
Young & Freedman Calc15th EditionUniversity PhysicsISBN: 9780135159552Non è quello che usi tu?Cambia libro di testo
Tutti i libri di testoYoung & Freedman Calc 15th EditionCh 09: Rotation of Rigid BodiesProblema 8a
Capitolo 9, Problema 8a

A wheel is rotating about an axis that is in the z-direction. The angular velocity ωz is -6.00 rad/s at t = 0, increases linearly with time, and is +4.00 rad/s at t = 7.00 s. We have taken counterclockwise rotation to be positive. Is the angular acceleration during this time interval positive or negative?

Guida verificata passo dopo passo
1
Determine the formula for angular acceleration (α). Angular acceleration is defined as the rate of change of angular velocity (ω) with respect to time (t). The formula is: α = ωf - ωit, where ωf is the final angular velocity, ωi is the initial angular velocity, and t is the time interval.
Substitute the given values into the formula. The initial angular velocity is ωi = -6.00 rad/s, the final angular velocity is ωf = +4.00 rad/s, and the time interval is t = 7.00 s.
Calculate the numerator of the formula, which is the change in angular velocity: ωf - ωi = 4.00 - (-6.00). Simplify this expression to find the total change in angular velocity.
Divide the change in angular velocity by the time interval to find the angular acceleration: α = 10.007.00. This will give the angular acceleration in rad/s².
Interpret the sign of the angular acceleration. Since the angular velocity is increasing from a negative value to a positive value, the angular acceleration is positive. This indicates that the wheel is speeding up in the counterclockwise direction.

Risposta video verificata per un problema simile:

Questa soluzione video è stata consigliata dai nostri tutor come utile per risolvere questo problema.
Durata del video:
1m

Concetti chiave

Ecco i concetti essenziali che devi comprendere per rispondere correttamente alla domanda.

Angular Velocity

Angular velocity is a vector quantity that represents the rate of rotation of an object around an axis. It is measured in radians per second (rad/s) and indicates both the speed and direction of the rotation. In this question, the angular velocity changes from -6.00 rad/s to +4.00 rad/s, indicating a change in the direction of rotation over time.
Video consigliato:
Percorso guidato
06:18
Intro to Angular Momentum

Angular Acceleration

Angular acceleration is the rate of change of angular velocity over time, typically measured in radians per second squared (rad/s²). It can be positive or negative, depending on whether the angular velocity is increasing or decreasing. In this scenario, the angular acceleration can be determined by analyzing the change in angular velocity from -6.00 rad/s to +4.00 rad/s over the time interval of 7 seconds.
Video consigliato:
Percorso guidato
12:12
Conservation of Angular Momentum

Direction of Rotation

The direction of rotation is crucial in determining the sign of angular velocity and angular acceleration. In this problem, counterclockwise rotation is defined as positive, while clockwise rotation is negative. The change in angular velocity from a negative to a positive value indicates a transition from clockwise to counterclockwise rotation, which implies that the angular acceleration must be positive during the time interval considered.
Video consigliato:
Percorso guidato
14:03
Rotational Position & Displacement
Pratica correlata
Domanda del libro di testo

A wheel is rotating about an axis that is in the z-direction. The angular velocity ωz is -6.00 rad/s at t = 0, increases linearly with time, and is +4.00 rad/s at t = 7.00 s. We have taken counterclockwise rotation to be positive. What is the angular displacement of the wheel at t = 7.00 s?

2174
views
Domanda del libro di testo

The angle θ through which a disk drive turns is given by θ(t) = a + bt - ct3, where a, b, and c are constants, t is in seconds, and θ is in radians. When t = 0, θ = π/4 rad and the angular velocity is 2.00 rad/s. When t = 1.50 s, the angular acceleration is 1.25 rad/s2. What are θ and the angular velocity when the angular acceleration is 3.50 rad/s2?

2103
views
Domanda del libro di testo

A bicycle wheel has an initial angular velocity of 1.50 rad/s. (a) If its angular acceleration is constant and equal to 0.200 rad/s2, what is its angular velocity at t = 2.50 s? (b) Through what angle has the wheel turned between t = 0 and t = 2.50 s?

1564
views
Domanda del libro di testo

A wheel is rotating about an axis that is in the z-direction. The angular velocity ωz is -6.00 rad/s at t = 0, increases linearly with time, and is +4.00 rad/s at t = 7.00 s. We have taken counterclockwise rotation to be positive. During what time interval is the speed of the wheel increasing? Decreasing?

1818
views
Domanda del libro di testo

The angle θ through which a disk drive turns is given by θ(t) = a + bt - ct3, where a, b, and c are constants, t is in seconds, and θ is in radians. When t = 0, θ = π/4 rad and the angular velocity is 2.00 rad/s. When t = 1.50 s, the angular acceleration is 1.25 rad/s2. (b) What is the angular acceleration when θ = π/4 rad?

2865
views
Domanda del libro di testo

The angle θ through which a disk drive turns is given by θ(t) = a + bt - ct3, where a, b, and c are constants, t is in seconds, and θ is in radians. When t = 0, θ = π/4 rad and the angular velocity is 2.00 rad/s. When t = 1.50 s, the angular acceleration is 1.25 rad/s2. Find a, b, and c, including their units.

1733
views