Explanation Given: The angular velocity, ω = 6 rad / s . The angular acceleration, α = 10 rad / s 2 . The position vector directed from B to A , r B / A = 0 .75 m . The radial distance, r = 0.3 m . Conclusion: Express the linear velocity of collar B in the fixed system. v B = ( − ω × r B / A ) i (I) Substitute 6 rad / s for ω and 0 .3 m for r B / A in Equation (I). v B = ( − 6 × 0.3 ) i = { − 1.8 i } m / s Express the acceleration vector of collar B in the fixed system. a B = − α ( r B / A ) i − ω 2 ( r B / A ) j (II) Substitute 10 rad / s 2 for α , 6 rad / s for ω and 0 .3 m for r B / A in Equation (II). a B = − 10 ( 0.3 ) i − ( 6 ) 2 ( 0.3 ) j = { − 3 i − 10.8 j } m / s 2 Write the motion of moving reference. v A = 0 a A = 0 Ω = ω A C = ω A C k Ω ˙ = α A C = α A C k Here, acceleration vector of A is a A , angular velocity is Ω , angular acceleration is Ω ˙ , angular velocity of A C is ω A C and angular acceleration of A C is α A C . Write the motion of collar A with respect to moving reference. r B / A = { 0.75 i } m ( v A / B ) x y z = ( υ A / B ) x y z i ( a A / B ) x y z = ( a A / B ) i Apply the relative velocity equation. v B = v A + Ω × r B / A + ( v A / B ) x y z (III) Here, linear velocity of A is v A . Substitute { − 1.8 i } m / s for v B , 0 for v A , ω A C k for Ω , { 0.75 i } m for r B / A and ( υ A / B ) x y z i for ( v A / B ) x y z in Equation (III). − 1.8 i = 0 + ( ω A C k ) × ( 0.75 i ) + ( υ A / B ) x y z i = − ( υ A / B ) x y z i + ( 0.75 ω A C ) j (IV) Equate i component from Equation (IV). − 1.8 i = − ( υ A / B ) x y z i ( υ A / B ) x y z = 1

Engineering Mechanics: Dynamics (14th Edition)

14th Edition

ISBN: 9780133915389

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 16.8, Problem 151P

To determine

The angular velocity ωAC and angular acceleration αAC of the slotted link AC .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 16.8, Problem 150P

Chapter 16.8, Problem 152P

Students have asked these similar questions

7. In the mechanism the piston rod has a horizontal velocity of v =8 ft/sec to the left as shown at the instant when e=ß= tan (4/3). Use the instantancous center scalar approach to determine the angular velocities of links AB and BC. NOTE: Locate the instant center of rotation: Clearly label the instantaneous center on the figure and show your calculation for its location from geometry. An (magnitude and direction) =, Wac (magnitude and direction) =

Disk B is at rest when it is brought into contact with disk A, which is rotating freely at 450 rpm clockwise. After 6 seconds of slippage, during which each disk has a constant angular acceleration, disk A reaches a final angular velocity of 140 rpm clockwise Disk radius a =3 in Disk radius b= 5 in. Determine the final linear speed at the point of contact between the disk in in/s

Determine the velocity of the rod R for any angle θ of cam C as the cam rotates with a constant angular velocity w. The pin connection at O does not cause an interference with the motion of plate A on C.

Chapter 16 Solutions

Engineering Mechanics: Dynamics (14th Edition)

Ch. 16.3 - Determine its constant angular acceleration and...Ch. 16.3 - Determine the angular acceleration when it has...Ch. 16.3 - Determine the time it takes to achieve an angular...Ch. 16.3 - If the angular displacement of the wheel is =...Ch. 16.3 - Determine the magnitude of the velocity and...Ch. 16.3 - Determine the velocity of the cylinder and the...Ch. 16.3 - Determine the magnitudes of the velocity and...Ch. 16.3 - If the disk is originally rotating at 0 = 12...Ch. 16.3 - It it is subjected to a constant angular...Ch. 16.3 - If it is subjected to a constant angular...

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 angular velocity ω A C and angular acceleration α A C of the slotted link A C .

Solution Summary: The author analyzes the angular velocity of the slotted link AC and its acceleration. The position vector directed from BtoA.

Concept explainers

Videos

The angular velocity ωAC and angular acceleration αAC of the slotted link AC .

Want to see the full answer?

Chapter 16 Solutions