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

∴ 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 .