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Chapter 14: Problem 1

State, or find out, which of the following are scalars and which are vectors: (a) the volume of a petrol tank, (b) a length measured in metres, (c) a length measured in miles, (d) the angular velocity of a flywheel, (e) the relative velocity of two aircraft, (f) the work done by a force, (g) electrostatic potential, (h) the momentum of an atomic particle.

Short Answer

Expert verified
Question: Identify whether the following quantities are scalars or vectors: (a) Volume of a petrol tank, (b) Length measured in metres, (c) Length measured in miles, (d) Angular velocity of a flywheel, (e) Relative velocity of two aircraft, (f) Work done by a force, (g) Electrostatic potential, (h) Momentum of an atomic particle. Answer: (a) Scalar, (b) Scalar, (c) Scalar, (d) Vector, (e) Vector, (f) Scalar, (g) Scalar, (h) Vector.

Step by step solution

01

(a) Volume of a petrol tank

The volume of a petrol tank only has a magnitude (measured in litres or gallons), and there is no associated direction. Thus, it is a scalar.
02

(b) Length measured in metres

A length measured in metres has a magnitude (the number of metres) but does not have a direction (since it's a pure distance, not a position). So, length is a scalar.
03

(c) Length measured in miles

Similar to (b), a length measured in miles has a magnitude, but no direction. Therefore, it is also a scalar.
04

(d) Angular velocity of a flywheel

Angular velocity has both a magnitude (the speed of rotation in radians per second or degrees per second) and a direction (the axis of rotation). Hence, it is a vector.
05

(e) Relative velocity of two aircraft

The relative velocity of two aircraft includes both a magnitude (speed difference) and a direction (the direction in which one aircraft is moving relative to the other). Therefore, it is a vector.
06

(f) Work done by a force

The work done by a force has only a magnitude (measured in joules) and no associated direction, as it is the product of force and the distance moved in the direction of the force. Thus, work done is a scalar.
07

(g) Electrostatic potential

Electrostatic potential has only a magnitude (measured in volts) and no associated direction. It is the amount of work needed to move a unit charge from one point to another in an electric field. Therefore, it is a scalar.
08

(h) Momentum of an atomic particle

The momentum of an atomic particle has both a magnitude (mass times velocity) and a direction (the direction of motion). Thus, momentum is a vector.

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