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Question
Pick out the two scalar quantities in the following list: force, angular momentum, work, current, linear momentum, electric field, average velocity, magnetic moment, relative velocity.
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Solution
Force: Force has magnitude as well as direction. The direction towards which the force is applied is known as the direction of force.
Force →F=m→a;→a = acceleration m = mass
Angular momentum: It is a vector quantity, and it is product of moment of inertia and the angular velocity about an axis.
It is represented by, →L=I→ω;I = moment of inertia →ω = angular velocity
Work done (W): Work is the product of the component of the force in the direction of the displacement and the magnitude of this displacement.
w=→F.→s;→F = Force, →s = displacement
W=Fscosθ;θ=angle between→F and →s. We know that the dot product of two quantities is always a scalar quantity.
Current: Current is a scalar quantity because current doesn’t obey the law of addition of vectors.
Linear momentum: Momentum is a vector quantity. It has both magnitude and direction. It is defined as →P=m→v; m = mass, →v = velocity
Electric field: Electric field is a vector quantity as it is defined as electric force per unit positive charge, and force is vector quantity. Hence electric field is also a vector quantity.
Average velocity: Average velocity is a vector; it has both magnitude and direction.
Average velocity is defined as total displacement divided by time.
Magnetic moment:
The magnetic moment is a vector relating torque of an object to the magnetic field. This is mathematically represented as:
→τ=→m×→B; →m = magnetic moment, →B = magnetic field
Relative velocity: Relative velocity is a vector quantity, it is velocity of an object with respect to the rest frame of another object.
In the given list in the question work and current are scalar quantities.
Force →F=m→a;→a = acceleration m = mass
Angular momentum: It is a vector quantity, and it is product of moment of inertia and the angular velocity about an axis.
It is represented by, →L=I→ω;I = moment of inertia →ω = angular velocity
Work done (W): Work is the product of the component of the force in the direction of the displacement and the magnitude of this displacement.
w=→F.→s;→F = Force, →s = displacement
W=Fscosθ;θ=angle between→F and →s. We know that the dot product of two quantities is always a scalar quantity.
Current: Current is a scalar quantity because current doesn’t obey the law of addition of vectors.
Linear momentum: Momentum is a vector quantity. It has both magnitude and direction. It is defined as →P=m→v; m = mass, →v = velocity
Electric field: Electric field is a vector quantity as it is defined as electric force per unit positive charge, and force is vector quantity. Hence electric field is also a vector quantity.
Average velocity: Average velocity is a vector; it has both magnitude and direction.
Average velocity is defined as total displacement divided by time.
Magnetic moment:
The magnetic moment is a vector relating torque of an object to the magnetic field. This is mathematically represented as:
→τ=→m×→B; →m = magnetic moment, →B = magnetic field
Relative velocity: Relative velocity is a vector quantity, it is velocity of an object with respect to the rest frame of another object.
In the given list in the question work and current are scalar quantities.
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