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#angular velocity

64 public questions tagged with this topic.

PHYSICS

The dimensional formula of angular velocity is [T^{-1] . Which quantity shares the same dimensions?

Given: The dimensional formula of angular velocity is [T^{-1] . Which quantity shares the same dimensions? These values define the system as per NCERT data. Formula: (a) [v / r] = [L T^{-1] / [L] = [T^{-1]. This is the standard NCERT relation for this phenomenon. Substitution & Calculation: (b) [a t] = [L T^{-2] [T] = [L T^{-1] . (c) [F / m] = [M L T^{-2] / [M] = [L T^{-2] . (d) [s / t] = [L] / [T] = [L T^{-1] . (a) matches. Result: The computed value matches the expected outcome and confirms the correct choice. Units and powers like J kg⁻¹ K⁻¹, m/s², 10⁻⁵ are properly used as per NCERT.

Ref: NCERT Physics Textbook for Class XI and XII, Chapter: Units and Measurements and Physical World, Topic: Dimensional analysis and fundamental principles.

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Moment of Inertia and Radius of Gyration

A wheel with moment of inertia 8kg m2 rotates at 2rad/s. A torque of 16Nm acts for 3s. What is its final angular velocit

α = τI = 168 = 2rad/s2. Δω = αt = 2×3 = 6rad/s. ω = ω0+Δω = 2+6 = 8rad/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 8 rad/s. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Moment of Inertia and Radius of Gyration

A wheel with moment of inertia 5kg m2 rotates at 3rad/s. A torque of 10Nm acts for 5s. What is its final angular velocit

α = τI = 105 = 2rad/s2. Δω = αt = 2×5 = 10rad/s. ω = ω0+Δω = 3+10 = 13rad/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 13 rad/s. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Moment of Inertia and Radius of Gyration

What happens to the angular velocity of a rigid body if the net external torque is zero?

If the net external torque is zero (dLdt = τ = 0), angular momentum is conserved, and for a fixed moment of inertia, angular velocity remains constant. As per NCERT, applying relevant law/formula with correct units and sign convention leads to It remains constant. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Moment of Inertia and Radius of Gyration

A thin ring of mass 3kg and radius 0.4m rotates about its center at 5rad/s. What is its rotational kinetic energy?

I = MR2 = 3×(0.4)2 = 0.48kg m2. K = 12Iω2 = 12×0.48×(5)2 = 0.24×25 = 6J. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 6.0 J. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Moment of Inertia and Radius of Gyration

A solid sphere of mass 6kg and radius 0.4m has an angular momentum of 11.52kg m2/s. What is its angular velocity?

I = 25MR2 = 25×6×(0.4)2 = 0.384kg m2. ω = LI = 11.520.384 = 30rad/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 30 rad/s. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Vector Product and Rotational Kinematics

A wheel with moment of inertia 6kg m2 rotates at 3rad/s. A torque of 12Nm acts for 3s. What is its final angular velocit

α = τI = 126 = 2rad/s2. Δω = αt = 2×3 = 6rad/s. ω = ω0+Δω = 3+6 = 9rad/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 9 rad/s. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Vector Product and Rotational Kinematics

A solid sphere of mass 5kg and radius 0.2m has an angular momentum of 8kg m2/s. What is its angular velocity?

I = 25MR2 = 25×5×(0.2)2 = 0.08kg m2. ω = LI = 80.08 = 100rad/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 100 rad/s. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Vector Product and Rotational Kinematics

A solid sphere of mass 5kg and radius 0.3m rotates about an axis through its center. If its angular momentum is 9kg m2/s

L = Iω. For a sphere: I = 25MR2 = 25×5×(0.3)2 = 0.18kg m2. ω = LI = 90.18 = 50rad/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 50 rad/s. This satisfies dimensional consistency and physical conditions given, so option C is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Vector Product and Rotational Kinematics

A solid sphere of mass 3kg and radius 0.1m rolls without slipping down an incline. If its linear speed is 5m/s, what is

For rolling without slipping: v = ωr. v = 5m/s, r = 0.1m. ω = vr = 50.1 = 50rad/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 50 rad/s. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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Vector Product and Rotational Kinematics

A solid sphere of mass 3kg and radius 0.4m has an angular momentum of 12kg m2/s. What is its angular velocity?

I = 25MR2 = 25×3×(0.4)2 = 0.192kg m2. ω = LI = 120.192≈62.5rad/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 62.5 rad/s. This satisfies dimensional consistency and physical conditions given, so option B is scientifically correct.

Ref: NCERT Class 11 Physics, Thermal Properties and Gravitation.

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