Question

A circular disc of mass 100 kg and radius of 0.8m makes 120 revolution per minute calculate a.angular velocity b. moment of inertia about the axis of rotation

Answer 1

Answer:

(a) The Angular velocity is 753.6 rad per min

(b) The moment of inertia about axis of a disc is 32 kg-m² .

Explanation:

Given as :

The mass of disc = m = 100 kg

The radius of disc = r = 0.8 meters

The number of revolution makes by disc = n = 120 rpm

Let The Angular velocity = ω  rad per min

Let The moment of inertia about axis = M.I  kg-m²

According to question

(a) Angular velocity = $\dfrac{number of revolution \times 2 \Pi }{time}$

Or, ω = 120 × 2 π

i.e ω = 120 × 2 × 3.14

Or , ω = 753.6 rad per min

So, The Angular velocity = ω  = 753.6 rad per min

Hence, The Angular velocity is 753.6 rad per min

(b) Moment of inertia = $\dfrac{1}{2}$ × mass × radius²

Or, M.I = = $\dfrac{1}{2}$ × m × r²

Or, M.I = = $\dfrac{1}{2}$ × 100 × (0.8) ²

∴ M.I = 32 kg-m²

So, The moment of inertia about axis of a disc = M.I = 32 kg-m²

Hence, The moment of inertia about axis of a disc is 32 kg-m² . Answer