Which of the following statements is true about the centripetal force acting on a mass m that is executing uniform circular motion?

1. It is perpendicular to the particle's acceleration

2. It is perpendicular to the particle's velocity

3. It is equal to the total tangential force acting on the particle

4. It is equal to the total force pointing towards the center of the circular path

5. All are true

Question

Which of the following statements is true about the centripetal force acting on a mass m that is executing uniform circular motion?

1. It is perpendicular to the particle's acceleration

2. It is perpendicular to the particle's velocity

3. It is equal to the total tangential force acting on the particle

4. It is equal to the total force pointing towards the center of the circular path

5. All are true

BlackTom AI · Accepted Answer

The problem asks about which statements are true regarding the centripetal force acting on a mass m in uniform circular motion. Let’s examine each option in turn, weighing what centripetal force is and how it relates to motion along a circle.

Option 1: 'It is perpendicular to the particle's acceleration.' In uniform circular motion, the acceleration (centripetal acceleration) points toward the center of the circle as well. The centripetal force is the net force toward the center that causes this acceleration, so it is not perpendicular to the acceleration; it is parallel to it. Therefore, this statement is false.

Option 2: 'It is perpendicular to the particle's velocity.' The velocity is tangential to the circular path, while the centripetal force is radial, pointing toward the center. A radial direction is indeed perpendicular to the tangential direction of velocity, so this statement is true.

Option 3: 'It is equal to the total tangential force acting on the particle.' In uniform circular motion, there is no tangential acceleration or tangential force; the motion is constant in speed, so the tangential force is zero. The centripetal force is not a tangential force; it is radial. Therefore, this statement is false.

Option 4: 'It is equal to the total force pointing towards the center of the circular path.' By definition, the centripetal force is the net (total) inward force that provides the centripetal acceleration toward the center. In uniform circular motion, the net inward force equals m v^2 / r and is the centripetal force. This statement is true.

Option 5: 'All are true.' Since options 1 and 3 are false (as explained above), this blanket claim is false.

Putting this together, we see that statements 2 and 4 accurately describe aspects of centripetal force in uniform circular motion, while statements 1, 3, and 5 are incorrect for the reasons given. The analysis shows how directionality (radial vs. tangential) and the concept of centripetal force as the inward net force clarify which statements hold true and which do not.

2025 Fall PHYS 2205 TR 11:00 - 12:15 _ 89122 PHYS 2205 Exam 2- Requires Respondus LockDown Browser

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