Skip to main content
Pearson+ LogoPearson+ Logo
Ch 09: Rotation of Rigid Bodies
Back
Previous problem
Next problem
All textbooksYoung & Freedman Calc 14th EditionCh 09: Rotation of Rigid BodiesProblem 9

Chapter 9, Problem 9

CALC A fan blade rotates with angular velocity given by ω_z(t) = g - bt^2, where g = 5.00 rad/s and b = 0.800 rad/s^3. (a) Calculate the angular acceleration as a function of time.

Verified Solution
Video duration:
1m
This video solution was recommended by our tutors as helpful for the problem above.
652
views
Was this helpful?

Video transcript

Welcome back everybody. We are given the formula for angular velocity as a function of time for some rotating particle. And it is given as follows, C. Which is a constant equal to 4.2 -3. Another constant equal to 0.25 times our time squared. And we need to find the angular acceleration as a function of time. Well this is going to be just the derivative of our angular velocity with respect to time. So let's go ahead and take the derivative of this equation right here, term by term derivative of 4.2, it's a constant. So it's just gonna be zero minus. We have this term that too is gonna come down in front times 0.5 Times are T. Which gives us that our angular acceleration as a function of time equal to negative 0. radiance per second cubed times time corresponding to our answer choice of Thank you all so much for watching. Hope this video helped. We will see you all in the next one.
Previous problemNext problem
Related Practice
Textbook Question
CALC The angle θ through which a disk drive turns is given by θ(t) = a + bt - ct^3, where a, b, and c are constants, t is in seconds, and θ is in radians. When t = 0, θ = p/4 rad and the angular velocity is 2.00 rad/s. When t = 1.50 s, the angular acceleration is 1.25 rad/s^2. (b) What is the angular acceleration when θ = p/4 rad?
1613
views
Textbook Question
CALC The angle θ through which a disk drive turns is given by θ(t) = a + bt - ct^3, where a, b, and c are constants, t is in seconds, and θ is in radians. When t = 0, θ = p/4 rad and the angular velocity is 2.00 rad/s. When t = 1.50 s, the angular acceleration is 1.25 rad/s^2. (c) What are θ and the angular velocity when the angular acceleration is 3.50 rad/s^2?
876
views
Textbook Question
CP CALC The angular velocity of a flywheel obeys the equation ω_z(t) = A + Bt2, where t is in seconds and A and B are constants having numerical values 2.75 (for A) and 1.50 (for B). (b) What is the angular acceleration of the wheel at (i) t = 0 and (ii) t = 5.00 s?
2002
views
Textbook Question
CALC A fan blade rotates with angular velocity given by ω_z(t) = g - bt^2, where g = 5.00 rad/s and b = 0.800 rad/s^3. (b) Calculate the instantaneous angular acceleration α_z at t = 3.00 s and the average angular acceleration α_av-z for the time interval t = 0 to t = 3.00 s. How do these two quantities compare? If they are different, why?
876
views
Textbook Question
You are a project manager for a manufacturing company. One of the machine parts on the assembly line is a thin, uniform rod that is 60.0 cm long and has mass 0.400 kg. (a) What is the moment of inertia of this rod for an axis at its center, perpendicular to the rod?
631
views
1
rank
Textbook Question
CALC A slender rod with length L has a mass per unit length that varies with distance from the left end, where x = 0, according to dm/dx = gx, where g has units of kg/m^2. (b) Use Eq. (9.20) to calculate the moment of inertia of the rod for an axis at the left end, perpendicular to the rod. Use the expression you derived in part (a) to express I in terms of M and L. How does your result compare to that for a uniform rod? Explain.
1392
views