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Difficulty: MediumNewton's Laws of Motion and Linear Momentum

If a constant magnitude net force continuously acts on a moving body strictly perpendicular to its direction of motion, the magnitude of the body's linear momentum remains constant while its direction of motion continuously changes.

Answer: Answer

Answer

The statement is True. A net force directed perpendicular to velocity changes only the direction of motion, keeping speed and the magnitude of linear momentum constant.
The statement is true because a force perpendicular to displacement does zero work, preserving kinetic energy and speed. Because speed is unchanged, the scalar magnitude of momentum remains constant while its vector direction curves continuously.

Step-by-Step Solution

1
Determine the work done by a perpendicular force.
The work done is W=FΔscos⁡(90∘)=0 JW = F \Delta s \cos(90^\circ) = 0\text{ J}.
Force perpendicular to displacement performs no work on the object.
2
Relate work done to speed and magnitude of linear momentum.
Zero work means zero change in kinetic energy, so speed vv is constant, making magnitude p=mvp = mv constant.
Linear momentum magnitude depends solely on mass and speed.
3
Evaluate the effect on momentum direction.
The force produces an acceleration vector perpendicular to velocity, changing the vector direction of linear momentum p⃗\vec{p}.
By Newton's Second Law (F⃗=dp⃗dt\vec{F} = \frac{d\vec{p}}{dt}), force dictates the rate of change of momentum vector.

Key Concept

Vector nature of linear momentum and perpendicular force action
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Topics

Newton's Laws of Motion and Linear Momentum

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