The motor turns gear A with an angular acceleration of A = 1.5 rad/s2 when the a

Question

The motor turns gear A with an angular acceleration of A = 1.5 rad/s2 when the angular velocity isA = 24 rad/s . (Figure 1)

Part A

Determine the angular velocity of gear D, measured counterclockwise.

Express your answer using three significant figures. Enter positive value if the angular velocity is counterclockwise and negative value if the angular velocity is clockwise.

Part B

Determine the angular acceleration of gear D, measured counterclockwise.

Express your answer using three significant figures. Enter positive value if the angular acceleration is counterclockwise and negative value if the angular acceleration is clockwise.

Figure 1 of 1

The motor turns gear A with an angular acceleration of A = 1.5 rad/s2 when the angular velocity isA = 24 rad/s . (Figure 1)

Part A

Determine the angular velocity of gear D, measured counterclockwise.

Express your answer using three significant figures. Enter positive value if the angular velocity is counterclockwise and negative value if the angular velocity is clockwise.

D =   rad/s  

Part B

Determine the angular acceleration of gear D, measured counterclockwise.

Express your answer using three significant figures. Enter positive value if the angular acceleration is counterclockwise and negative value if the angular acceleration is clockwise.

D =   rad/s2  

Figure 1 of 1

Explanation / Answer

Part A)

This part of the problem can be solved using the conservation of angular momentum

Li = Lf

gears A y B

IA WA = IB WB

The moment of inertia of a cylinder with an axis passing through the center is

I = ½ M R2

WB = WA IA/IB

WB= WA½ M RA2/ ½ M RB2

We must assume that the masses of the gears are the same as they do not give the value of the same

WB= WA(RA/RB)2

WB= 24 (4/10)2

WB = 3.84 rad/s

A gear rotate them gears B and C are the same axis one two thus rotate with the same WB= WC

and is the same sense

gear C y D

Li =Lf

IC WC = ID WD

WD = WC IC/ID

WD = WC (RC/RD)2

WD= 3.84 ( 5/10)2

WD =0.960 rad/s

As the gear B and C rotate clockwise gears D rotate in the opposite direction that is counterclockwise

Part B)

We use the expression of angular momentum for each gear

= I

Engranaje A

A = IA A

A = IA A

B = IB B

like the gears they are attached torque is the same in all of them

IAA= IBB

B= IA/IBA

gear B and C rotate together along the same axis thus has the same angular acceleration

IC C = ID D

D = C IC /ID

D = IA /IB A IC /ID

D= (RARC/RBRD)2A

D= ( 4 5 / 10 10)21.5

D= 0.0600 Rad/s2

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