wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A pinion with radius r1, and inertia I1 is driving a gear with radius r2 and inertia I2. Torque τ1 is applied on pinion. The following are free body diagrams of pinion and gear showing important forces (F1 and F2) of interaction. Which of the following relations hold true?

A
F1F2;τ1=I1¨θ;F2=I2r1r22¨θ1
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
F1=F2;τ1=I1[I1+I2(r1r2)2]¨θ;F2=I2r1r22¨θ1
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
F1=F2;τ1=I1¨θ1;F2=I21r2¨θ2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
F1F2;τ1=I1[I1+I2(r1r2)2]¨θ1;F2=I21r2¨θ2
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B F1=F2;τ1=I1[I1+I2(r1r2)2]¨θ;F2=I2r1r22¨θ1
τ1F1r1=I1¨θ1...(i)

F1=F2..(ii)

[Action and reaction are equal by Newton's 3rd law]

F2r2=τ=I2¨θ2...(iii)

From equations (ii) and (ii)

F2=F1=I2¨θ2r2...(iv)

From equations (i) and (iv)

τ1(I2¨θ2r2)r1=I1¨θ1...(v)

We know, r1ω1=r2ω2

r1˙θ1=r2˙θ2

Differentiating with respect to time

r1¨θ1=r2¨θ2

¨θ2=r1r2¨θ1

τ1=I1¨θ1+I2r2[r1r2¨θ1]r1

τ1=[I1+I2[r1r2]2]¨θ1

τ2=I2¨θ2=F2r2

F2=I2r2¨θ2=I2r2[r1r2¨θ1]

F2=I2r1r22¨θ1

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Newton's 2nd Law Applied to Rigid Bodies
ENGINEERING MECHANICS
Watch in App
Join BYJU'S Learning Program
CrossIcon