First slide

Thermal expansion

Question

Effect of moment of inertia of a rigid body due to thermal expansion is $\frac{Δ I}{I} = x α Δ t$ where $x =$ $(w h e r e I i s m o m e n t o f i n e r t i a; ∆ I i s c h a n g e i n m o m e n t o f i n e r t i a; α i s c o e f f i c i e n t o f l i n e a r e x p a n s i o n o f s o l i d; ∆ t i s c h a n g e i n t e m p e r a t u r e)$

Moderate

A

1
B

2
C

3
D

4

Solution

$m o m e n t o f i n e r t i a I = m K^{2} m i s m a s s; K i s r a d i u s o f g y r a t i o n o n d i f f e r e n t i a t i n g a b o v e e q u a t i o n a n d d i v i d i n g s a m e w i t h a b o v e e q u a t i o n \frac{∆ I}{I} = 2 \frac{∆ K}{K} f r a c t i o n a l c h a n g e i n m o m e n t o f i n e r t i a i s \frac{∆ I}{I} = 2 α ∆ t α i s c o e f f i c i e n t o f l i n e a r e x p a n s i o n o f s o l i d ∆ t i s c h a n g e i n t e m p e r a t u r e$

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