#linear velocity

Vector Product and Rotational Kinematics

In rotational motion, what is the relationship between linear velocity and angular velocity for a particle?

The linear velocity v of a particle in rotational motion is related to angular velocity ω by v = ωr, where r is the perpendicular distance from the axis. As per NCERT, applying relevant law/formula with correct units and sign convention leads to v\=ωr. 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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Rotational Kinetic Energy and Dynamics

What happens to the linear velocity of a particle as its distance from the axis of rotation increases?

Linear velocity v = ωr increases with distance r from the axis because angular velocity ω is constant for a rigid body, and v is directly proportional to r. As per NCERT, applying relevant law/formula with correct units and sign convention leads to It increases. 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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Rotational Kinetic Energy and Dynamics

In rolling motion of a rigid body without slipping, what is the relationship between linear and angular velocity?

For rolling without slipping, the linear velocity of the center of mass (v) equals the product of angular velocity (ω) and radius (r): v = ωr. As per NCERT, applying relevant law/formula with correct units and sign convention leads to v\=ωr. 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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Rotational Kinetic Energy and Dynamics

A particle moves in a circle of radius 0.5m with an angular velocity of 4rad/s. What is the magnitude of its linear velo

Linear velocity: v = ωr. ω = 4rad/s, r = 0.5m. v = 4×0.5 = 2m/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 2 m/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 3kg block moves with a velocity of 5m/s along the y-axis. What is the magnitude of the velocity of its center of mass?

For a single object, the velocity of the center of mass is the same as the object’s velocity. Velocity = 5m/s along y-axis, magnitude = 5m/s. As per NCERT, applying relevant law/formula with correct units and sign convention leads to 5 m/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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