In uniform circular motion, which of the following quantities are constant? Check all that apply: centripetal acceleration the magnitude of the net force instantaneous velocity speed
The Correct Answer and Explanation is:
Correct Answers:
- ✅ The magnitude of the net force
- ✅ Speed
Explanation
In uniform circular motion, an object moves along a circular path at a constant speed. Despite the speed being constant, the object is continuously changing direction. This directional change means the object is accelerating, even though its speed remains unchanged. This specific type of acceleration, called centripetal acceleration, always points toward the center of the circle.
Let’s examine each of the given quantities:
- Centripetal Acceleration:
While the magnitude of centripetal acceleration is constant in uniform circular motion (since speed and radius remain constant), its direction changes continuously as the object moves along the circle. Since acceleration is a vector, and its direction changes, centripetal acceleration is not constant in the vector sense — only its magnitude is. - The Magnitude of the Net Force:
The net force acting on an object in uniform circular motion is directed toward the center of the circle and is called centripetal force. Just like acceleration, its direction changes continuously. However, the magnitude of this net force remains constant because it depends on mass, speed, and radius, all of which are constant in uniform circular motion. F=mv2rF = \frac{mv^2}{r}F=rmv2 Therefore, the magnitude of the net force is constant. - Instantaneous Velocity:
Velocity is a vector quantity, meaning it has both magnitude and direction. Although the magnitude (speed) remains constant, the direction of velocity changes continuously. Therefore, instantaneous velocity is not constant. - Speed:
Speed is the scalar magnitude of velocity and remains constant throughout uniform circular motion, as the object covers equal distances in equal time intervals along the circular path.
Conclusion:
In uniform circular motion, the speed and the magnitude of the net force are constant, while instantaneous velocity and centripetal acceleration (as vectors) are not.
