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Zorluk: ZorNewton's Laws of Motion and Linear Momentum

For an object of constant mass moving at constant speed along a complete circular path, the net vector impulse imparted to the object over one full revolution is zero, even though a continuous centripetal force acts on the object throughout the motion.

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The statement is true because the impulse-momentum theorem states that net impulse equals the change in momentum (J⃗=Δp⃗\vec{J} = \Delta \vec{p}). After one full revolution, the object's initial and final velocity vectors are identical, resulting in zero change in momentum.
The statement is correct because linear momentum is a vector quantity. Over a complete circular revolution, the initial and final velocity vectors are identical in both magnitude and direction, making the change in momentum—and therefore the net vector impulse—equal to zero.

Adım Adım Çözüm

1
Recall the vector definition of impulse and the impulse-momentum theorem.
The net impulse J⃗\vec{J} acting on a body equals its change in linear momentum: J⃗=Δp⃗=p⃗f−p⃗i=mv⃗f−mv⃗i\vec{J} = \Delta \vec{p} = \vec{p}_f - \vec{p}_i = m\vec{v}_f - m\vec{v}_i.
Impulse is a vector quantity dependent on the initial and final states of momentum over the time interval.
2
Evaluate the velocity vector of the object after one complete circular revolution at constant speed.
Since the speed is constant and the trajectory completes a closed loop, the final velocity vector v⃗f\vec{v}_f has the exact same magnitude and direction as the initial velocity vector v⃗i\vec{v}_i.
A complete revolution returns the object to its starting point with its velocity pointing in the initial direction.
3
Calculate the change in momentum Δp⃗\Delta \vec{p}.
Δp⃗=m(v⃗f−v⃗i)=m(0)=0⃗\Delta \vec{p} = m(\vec{v}_f - \vec{v}_i) = m(0) = \vec{0}. Thus, net impulse J⃗=0⃗\vec{J} = \vec{0}.
Subtracting identical vectors yields zero vector magnitude.

Anahtar Kavram

Impulse-Momentum Theorem and Vector Nature of Linear Momentum
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Newton's Laws of Motion and Linear Momentum

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