In uniform circular motion, which of the following quantities are constant: speed, instantaneous velocity, centripetal acceleration, the magnitude of the net force?
The Correct Answer and Explanation is:
Correct Answer: Speed and the magnitude of the net force are constant.
Explanation (300+ words):
Uniform circular motion refers to the motion of an object traveling in a circular path at a constant speed. Although the speed remains the same, the direction of motion continuously changes due to the circular path. This change in direction causes a change in velocity and requires a net force, called the centripetal force, to keep the object moving in a circle.
Let’s break down the quantities mentioned:
- Speed – Constant
Speed is a scalar quantity that measures how fast an object is moving, regardless of direction. In uniform circular motion, the magnitude of velocity (i.e., speed) remains unchanged throughout the motion. So speed is constant. - Instantaneous Velocity – Not Constant
Velocity is a vector quantity, meaning it has both magnitude and direction. While the speed (magnitude of velocity) is constant, the direction of velocity is continuously changing because the object is always turning. Therefore, instantaneous velocity is not constant. - Centripetal Acceleration – Not Constant in Direction, but Magnitude is Constant
Centripetal acceleration always points toward the center of the circle and is responsible for changing the direction of the velocity. Its magnitude is given by $a_c = \frac{v^2}{r}$, where $v$ is the constant speed and $r$ is the radius of the circle. Because both $v$ and $r$ are constant in uniform circular motion, the magnitude of centripetal acceleration is constant, but its direction changes constantly, following the direction toward the center at each point on the path. - Magnitude of the Net Force – Constant
The net force required to keep the object in circular motion is the centripetal force, which has a constant magnitude given by $F = \frac{mv^2}{r}$. Since both $m$ and $v$ are constant, and the radius $r$ doesn’t change, the magnitude of the net force is constant. However, like acceleration, the direction of the net force also changes continuously, always pointing toward the center.
Summary:
- Constant: Speed, Magnitude of Net Force
- Not Constant: Instantaneous Velocity, Direction of Centripetal Acceleration
