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System of Particles and Rotational Motion

Rotational Dynamics

A disc of mass 2 {~kg} and radius 0.2 {~m} is rotating with an

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Easy

Solving time: 2 mins

A disc of mass $2 kg$ and radius $0.2 m$ is rotating with angular velocity $30 rads^{- 1}$ .
What is angular velocity, if a mass of $0.25 kg$ is put on periphery of the disc?

24 rads^{- 1}

36 rads^{- 1}

15 rads^{- 1}

26 rads^{- 1}

Views: 6,145 students

Updated on: Apr 1, 2023

Found 3 tutors discussing this question

Henry Discussed

A disc of mass

2 kg

and radius

0.2 m

is rotating with angular velocity

30 rads^{- 1}

.
What is angular velocity, if a mass of

0.25 kg

is put on periphery of the disc?

8 mins ago

Discuss this question LIVE

8 mins ago

Text solutionVerified

If no external torque acts on a system of particle th momentum of the system remains constant, that is,

τ = 0

\frac{d L}{d t} = 0

L = I ω =

constant

\Rightarrow I_{1} ω_{1} = I_{2} ω_{2}

\Rightarrow \frac{1}{2} M r^{2} ω_{1} = \frac{1}{2} (M + 2 m) r^{2} ω_{2}

.............(i)

∴

Here,

M = 2 kg, m = 0.25 kg, r = 0.2 m

ω_{1} = 30 rads^{- 1}

Hence, we get after putting the given values in Eq. (i)

\frac{1}{2} \times 2 \times (0.2)^{2} \times 30 = \frac{1}{2} \times (2 + 2 \times 0.25) (0.2)^{2}

ω_{2}

\Rightarrow ∴ 60 = 2.5 ω_{2} ω_{2} = 24 rads^{- 1}

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Question Text	A disc of mass $2 kg$ and radius $0.2 m$ is rotating with angular velocity $30 rads^{- 1}$ . What is angular velocity, if a mass of $0.25 kg$ is put on periphery of the disc?
Updated On	Apr 1, 2023
Topic	System of Particles and Rotational Motion
Subject	Physics
Class	Class 11
Answer Type	Text solution:1 Video solution: 3
Upvotes	365
Avg. Video Duration	10 min

A disc of mass $2 kg$ and radius $0.2 m$ is rotating with angular velocity $30 rads^{- 1}$ .
What is angular velocity, if a mass of $0.25 kg$ is put on periphery of the disc?

Text solutionVerified

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A disc of mass 2 kg and radius 0.2 m is rotating with angular velocity 30rads−1. What is angular velocity, if a mass of 0.25 kg is put on periphery of the disc?

Text solutionVerified

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A disc of mass $2 kg$ and radius $0.2 m$ is rotating with angular velocity $30 rads^{- 1}$ .
What is angular velocity, if a mass of $0.25 kg$ is put on periphery of the disc?