Explanation Given: The radius of the propeller P , gears A and B is shown in Figure (1). The angular acceleration α is ( 300 t ) rad/s 2 . The radius of the gear A is 0.7 in . . The radius of the gear B is 1.4 in . . The radius of the propeller P is 2.20 in . . The time t is 0.75 s . Write the equation for the angular acceleration. α A = ( 300 t ) rad/s 2 (I) Write the expression for the angular acceleration. α = d ω d t d ω = α d t (II) Here, angular acceleration is α and rate of change of angular velocity with respect to time is ( d ω d t ) . Since, gear B is in mesh with gear A . Write the expression angular velocity ω B of gear B and ω A of gear A . ω A r A = ω B r B ω B = r A r B ω A (III) Here, angular velocity of gear A is ω A , angular velocity of gear B is ω B , radius of gear B is r B and radius of gear A is r A . Write the expression angular acceleration α B of gear B and α A of gear A . α A r A = α B r B α B = r A r B α A (IV) Here, angular acceleration of gear A is α A , angular acceleration of gear B is α B , radius of gear B is r B and radius of gear A is r A . Write the expression for the magnitude of the velocity. υ P = ω B r P (V) Here, velocity is υ A , angular velocity ω and radius is r A . Write the expression of tangential acceleration. a t = α B r P (VI) Here, tangential acceleration is ( a A ) t , angular acceleration is α , and radius is r A . Write the expression of normal acceleration. a n = ω B 2 r P (VII) Here, normal acceleration is ( a A ) n , angular velocity is ω and radius is r A . Write the expression for the magnitude of acceleration. a P = ( a t 2 ) + ( a n 2 ) (VIII). Here, acceleration is a B , tangential acceleration is a t and normal acceleration is a n . Conclusion: Substitute ( 300 t ) rad/s 2 for α in Equation (II). Integrate the Equation (II) at the limits 0 to ω A for ω and 0 to 0.75 s for t . ∫ 0 ω A d ω = ∫ 0 0.75 ( 300 t ) rad/s 2 d t [ ω ] 0 ω A = [ 200 t 3 / 2 ] 0 0

Engineering Mechanics: Statics & Dynamics (14th Edition)

14th Edition

ISBN: 9780133915426

Author: Russell C. Hibbeler

Publisher: PEARSON

See similar textbooks

Concept explainers

Conservation of Energy

In physics, the rule of the conservation of energy states that energy doesn’t disappear from the atmosphere; instead, it changes its form from one type to another. Energy is one of the most important physical quantities in nature, and it cannot be create…

Videos

Question

Chapter 16.3, Problem 28P

To determine

The magnitude of the velocity and acceleration of point P at tip of the propeller when time t is 0.75 s .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 16.3, Problem 27P

Chapter 16.3, Problem 29P

Students have asked these similar questions

(read image) (Answer: M motor = 0.836 Ib-ft, Mf = 0.1045 Ib-ft)

Please find the torsional yield strength, the yield strength, the spring index, and the mean diameter.

(read image) (Answer Given)

Chapter 16 Solutions

Engineering Mechanics: Statics & Dynamics (14th Edition)

Ch. 16.3 - When the gear rotates 20 revolutions, it achieves...Ch. 16.3 - The flywheel rotates with an angular velocity of ...Ch. 16.3 - The flywheel rotates with an angular velocity of (...Ch. 16.3 - The bucket is hoisted by the rope that wraps...Ch. 16.3 - A wheel has an angular acceleration of = (0.5 )...Ch. 16.3 - For a short period of time, the motor turns gear A...Ch. 16.3 - Prob. 1P Ch. 16.3 - The angular acceleration of the disk is defined by...Ch. 16.3 - The disk is originally rotating at 0 = 12 rad/s....Ch. 16.3 - Prob. 4P

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The magnitude of the velocity and acceleration of point P at tip of the propeller when time t is 0.75 s .

Solution Summary: The magnitude of velocity and acceleration of point P at the tip of the propeller when time t is 0.75 is shown in Figure (1).

Concept explainers

Videos

The magnitude of the velocity and acceleration of point P at tip of the propeller when time t is 0.75 s .

Want to see the full answer?

Chapter 16 Solutions