Question

derive the expression for kinetic energy of a rotating rigid body​

Answer 1

Answer:

Consider a rigid body rotating with a constant angular velocity  

ω

 about an axis passing through the point O.

As the body rotates, all the particles perforM  uniform circular motion.

The linear speed of the particle with mass m  

​ otal Rolling kinetic energy=Translational K.E+Rotational K.E

=  

2

1

​  

MV  

2

+  

2

1

​  

Iω  

2

 

But ω=  

R

V

​  

 

K.E=  

2

1

​  

MV  

2

+  

2

1

​  

I(  

R

V

​  

)  

2

 

=  

2

1

​  

MV  

2

+  

2

1

​  

I(  

R  

2

 

V  

2

 

​  

)

For solid sphere I=  

5

2

​  

MR  

2

 

K.E=  

2

1

​  

MV  

2

+  

2

1

​  

×  

5

2

​  

MR  

2

×(  

R  

2

 

V  

2

 

​  

)

=  

2

1

​  

MV  

2

+  

5

1

​  

MV  

2

 

=  

10

7

​  

MV  

2