D. The acceleration vector of the planet points toward the center of the circle.
Explanation:
An object is said to be in uniform circular motion if:
- It is moving along a circular trajectory, and
- Its speed during the motion is constant
Here we have a planet orbiting a star in uniform circular motion. We can analyze each of the statements given:
A. The velocity vector of the planet points toward the center of the
circle --> FALSE. At each moment of the motion, the velocity vector always points tangent to the circle, not towards its centre.
B. The speed of the planet is always changing. --> FALSE. According to the definition of uniform circular motion, the speed does not change during the motion. However, the velocity changes (because velocity is a vector, so its direction changes; but speed is a scalar, so its value does not change)
C. The velocity of the planet is constant. --> FALSE. As we said previously, velocity is a vector, so it has both magnitude and direction. While its true that its magnitude does not change, its direction changes (because the planet is moving in a circle)
D. The acceleration vector of the planet points toward the center of
the circle. --> TRUE. The acceleration of an object in uniform circular motion is called centripetal acceleration, and it has the same direction of the force that is keeping the object in circular motion: in this case, it is the gravitational force, which points towards the centre of the circle.
Learn more about circular motion:
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