Merry-Go-Round Motion: Understanding Acceleration

When a boy is enjoying a ride on a merry-go-round, even if it is moving with a constant speed of $10 \text{ ms}^{-1}$, his motion is not simply uniform. To understand this, we need to differentiate between speed and velocity, and how they relate to acceleration, especially in circular motion.

Speed vs. Velocity in Merry-Go-Round Physics

• Speed: Speed is a scalar quantity, meaning it only has magnitude. In this case, the merry-go-round's speed is constant at $10 \text{ ms}^{-1}$. This means the rate at which the boy covers distance along the path is fixed.
• Velocity: Velocity is a vector quantity, meaning it has both magnitude (speed) and direction. While the boy's speed might be constant, his direction of motion is continuously changing as he moves in a circle on the merry-go-round.

Acceleration in Circular Motion

Acceleration is defined as the rate of change of velocity. Since velocity is a vector quantity, a change in either its magnitude (speed) or its direction, or both, results in acceleration.

• In the case of the merry-go-round, the boy's speed is constant. However, his direction of motion is constantly changing as he moves along the circular path.
• Because the direction of the boy's velocity is continuously changing, his velocity itself is changing, even if the speed remains constant.
• A change in velocity implies the presence of acceleration. This type of acceleration, which is directed towards the center of the circular path, is known as centripetal acceleration.
• The formula for centripetal acceleration ($a_c$) is given by: $a_c = \frac{v^2}{r}$ where $v$ is the speed and $r$ is the radius of the circular path. Since $v$ is non-zero, and $r$ is finite, there will always be a non-zero centripetal acceleration in uniform circular motion.

Analyzing the Options for Merry-Go-Round Motion

• at rest: This option is incorrect because the boy is clearly moving with a speed of $10 \text{ ms}^{-1}$, not stationary.
• in accelerated motion: This option is correct. Despite having a constant speed, the boy's direction of motion is continuously changing due to the circular path of the merry-go-round. This constant change in direction means his velocity is changing, which implies he is undergoing acceleration (specifically, centripetal acceleration).
• moving with no acceleration: This option is incorrect. As explained, a change in the direction of velocity means there is acceleration, even if the speed is constant.
• moving with uniform velocity: This option is incorrect. Uniform velocity implies both constant speed AND constant direction. Since the direction of motion is constantly changing on a merry-go-round, the velocity is not uniform.

Therefore, even with a constant speed, the boy on the merry-go-round is in accelerated motion due to the continuous change in the direction of his velocity.