Question

the rotational kinetic energy of a body is given by E= 1/2 Iw​2, where w is angular velocity of the body. Use this equation to get dimensional formula for I.

Answer 1

Dimensional formula for {E} is {M^2L^2T^-2}
unit of w be rad/sec and rad being dimensionless so,
{w} = {T^-1}
and from the formula we can say that I=2K/w^2
so {I} = {K}/{w}^2
{I} = {ML^2} Answer
HOPE IT HELPED

Answer 2

Answer:

The dimensional formula of the moment of inertia(I) is [ML²].

Explanation:

The rotational kinetic energy of a body is given by,

$E=\frac{1}{2}I\omega^2$     (1)

Where,

E=rotational kinetic energy of a body

I=moment of inertia of the body

ω=angular velocity of the body

We can also write equation (1) as,

$I=\frac{2E}{\omega^2}$       (2)

The dimensional formula of energy(E) is given as=[ML²T⁻²]

The dimensional formula of angular velocity(ω) is given as=[T⁻¹]

By placing the required entities in equation (2) we get;

$I=\frac{ML^2T^-^2}{[T^-^1]^2}$

$I=\frac{ML^2T^-^2}{T^-^2}$

$I=[ML^2]$

The dimensional formula of the moment of inertia(I) is [ML²].

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