Question

Derive rotational kinetic energy dimensional formula

Answer 1

Answer:

$translational \: kinetic \: energy \: = m \: v ^{2} \times \frac{1}{2}$

$rotatinal \: k.e. = \frac{1}{2} \times i \: \times w ^{2}$

I = roatatinal mass = m * r^2,

W = angular speed = v / r.

Dimensional Formula =

${ m v ^{2} )$

Answer 2

$\huge\sf{\underline{\underline{\pink{Answer:-}}}}$

Total kinetic Energy of rotating object is the sum of kinetic energy of all individual particles of an object. so Rotational kinetic energy (KR) = ∑ 1/2 (mv2) = 1/2 ∑ (m r2 ω2) = 1/2 (∑ m r2) ω2. We can also write it as KR = 1/2 Iω2. ——- (Moment of Inertia (I)= ∑ m r2 )