A Motor Gives Gear A An Angular Acceleration Of A PDF

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Question: A motor gives gear A an angular acceleration of ?A=(2t^3)rad/… (19 bookmarks)

A motor gives gear A an angular acceleration of ?A=(2t^3)rad/s2, where t is in seconds. If this gear is initially turning at ?A = 25 rad/s , determine the angular velocity of gear B when t = 3 s, measured counterclockwise.

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Step 1 of 2

Vector Mechanics...

Write the equation for angular acceleration of gear A:

…… (1) Here, is the angular acceleration of gear A and Integrate equation (1):

is the angular velocity of gear A.

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Explanation | Common mistakes | Hint for next step Write the equation for angular acceleration of gear A. Thereafter, integrate this equation with 0 seconds and t seconds as time limits. Rearrange the products of integration and hence, nd the equation for angular velocity of gear A after t seconds. 

Step 2 of 2 Write the relation between the linear velocities of gears A and B:

Here,

is the radius of gear A,

Substitute

for

,

is the radius of gear B and

for

, and

is the angular speed of gear B.

for

,

for

Therefore, the angular velocity of gear B is

, and 3 seconds for .

.

Explanation | Common mistakes Write the relation between the linear velocities of gears A and B. Substitute the values of all the variables and calculate the linear velocity of gear B after 3 seconds.

Answer Therefore, the angular velocity of gear B is

.

Practice with similar questions Q: A motor gives gear A an angular acceleration of αA=(2t3)rad/s2, where t is in seconds. If this gear is initially turning at ωA = 17 rad/s ,determine the angular velocity of gear B when t = 3 s, measured counterclockwise. A: See answer

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