An object is in uniform circular motion. Identify the correct statement(s).

(1) Its acceleration is constant.

(2) Its radial acceleration component is constant in magnitude.

(3) Its tangential acceleration component is non-zero and constant in magnitude.

Question

An object is in uniform circular motion. Identify the correct statement(s).

(1) Its acceleration is constant.

(2) Its radial acceleration component is constant in magnitude.

(3) Its tangential acceleration component is non-zero and constant in magnitude.

BlackTom AI · Accepted Answer

Let's parse the scenario: an object in uniform circular motion means it travels along a circle at a constant speed with a fixed radius. Now, examine each option in light of this.
Option (2) states that the radial (centripetal) acceleration component is constant in magnitude. For circular motion, the magnitude of the centripetal acceleration is a_r = v^2 / r, which depends only on the constant speed v and fixed radius r. Since both v and r are constant, a_r remains constant in magnitude. This option is consistent with the standard description of uniform circular motion.
Option (1) claims that the acceleration is constant. Here’s the subtlety: although the magnitude of the centripetal acceleration is constant, the direction of the acceleration vector continually points toward the center of the circle and thus changes as the particle moves around the path. Because the acceleration vector is not fixed in direction, the acceleration is not constant in the vector sense. If someone interprets "constant" to mean the vector, this statement is false; if they mean the magnitude, it would be true, but the usual interpretation in physics asks about the vector quantity.
Option (3) asserts that the tangential acceleration component is non-zero and constant. In uniform circular motion, the speed is constant, so there is no tangential acceleration (a_t = dv/dt = 0). Therefore, this option is incorrect on both the non-zero and the constant aspects.
Putting the pieces together, the only statement that aligns with the physics of uniform circular motion is that the radial acceleration magnitude is constant, while the other statements mischaracterize either the vector nature of acceleration or the presence of tangential acceleration.

SPHY001 Graded Quiz 3 (Unit 5 and Unit 6)- Requires Respondus LockDown Browser

An object is in uniform circular motion. Identify the correct statement(s). (1) Its acceleration is constant. (2) Its radial acceleration component is constant in magnitude. (3) Its tangential acceleration component is non-zero and constant in magnitude.

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