Question

when the angular velocityof body change from 16 rad/s to 30 rad/s the angular momentum changes by 100 kgmsquar/s what is the change in KE of the body​

Answer 1

Given :-

• Initial angular velocity (ω1) = 16 rad/s
• Final angular velocity (ω2) = 30 rad/s
• Change in momentum (Δp) = 100 kg.m²/s

To Find :-

• The change in K.E of the body.

Solution :-

We know that,

Change in momentum = I(ω2) - I(ω1)

[ Put the values ]

⟹ Δp = I(ω2 - ω1 )

⟹ 100 = I(30 - 16)

⟹ 100 = I(14)

⟹ I = 100/14

⟹ I = 7.1 kgm²

Now, we need to find change in kinetic energy of the body.

So,

Change in kinetic energy = ¹/2 × I(ω2)² - ¹/2 × I(ω1)²

[ Put the values ]

⟹ ΔK.E = ¹/2 × 7.1 × 30² - ¹/2 × 7.1 × 16²

⟹ ΔK.E = 3.55 × 900 - 3.55 × 256

⟹ ΔK.E = 3195 - 908.6

⟹ ΔK.E = 2286.4 J

Therefore,

The change in K.E of the body is 2286.4 Joule.

Answer 2

Question :-

When the angular velocityof body change from 16 rad/s to 30 rad/s the angular momentum changes by 100 kgmsquar/s what is the change in KE of the body.

Answer :-

• The change in K.E of the body is 2286.4 Joule.

Given :-

• Angular velocityof body change from 16 rad/s to 30 rad/s.
• The angular momentum changes by 100 kgmsquare/s.

Have to Find :-

What is the change in KE of the body ?

Calculations :-

As we all know the formula :-

From given we know :-

• (Δp) = 100 kg.m²/s
• (ω1) = 16 rad/s
• (ω2) = 30 rad/

Here ,

" (Δp) " Change in momentum

" (ω1) " Initial angular velocity

"(ω2) " Final angular velocity

Now ,

Change in momentum = I(ω2) - I(ω1)

Simply substituting the values in the above formula :-

↠ Δp = I(ω2 - ω1 )

↠ 100 = I(30 - 16)

↠ 100 = I(14)

↠ I = 100/14

↠ I = 7.1 kgm²

Now , we have all the required values , let's find out kinetic energy now :-

↠ Change in kinetic energy = 1/2 × I(ω2)² - 1/2 × I(ω1)²

↠ ΔK.E = 1/2 × 7.1 × 30² - 1/2 × 7.1 × 16²

↠ ΔK.E = 3.55 × 900 - 3.55 × 256

↠ ΔK.E = 3195 - 908.6

↠ ΔK.E = 2286.4 J

Hence ,

ΔK.E = 2286.4 J is the required Answer .