Questions: A man, with his arms at his sides, is spinning on a light frictionless turntable. When he extends his arms: his rotational kinetic energy increases his angular velocity increases his angular momentum remains the same his angular velocity remains the same his rotational inertia decreases

A man, with his arms at his sides, is spinning on a light frictionless turntable. When he extends his arms:
his rotational kinetic energy increases
his angular velocity increases
his angular momentum remains the same
his angular velocity remains the same
his rotational inertia decreases

Transcript text: A man, with his arms at his sides, is spinning on a light frictionless turntable. When he extends his arms: his rotational kinetic energy increases his angular velocity increases his angular momentum remains the same his angular velocity remains the same his rotational inertia decreases

Solution

Solution Steps

Step 1: Understanding the Problem

We need to determine what happens to various physical quantities when a man spinning on a frictionless turntable extends his arms. The quantities in question are rotational kinetic energy, angular velocity, angular momentum, and rotational inertia.

Step 2: Analyzing Angular Momentum

Angular momentum (\(L\)) is conserved in a closed system with no external torques. The man and turntable system is isolated, so: \[ L = I \omega \] where \(I\) is the moment of inertia and \(\omega\) is the angular velocity. Since no external torques act on the system, \(L\) remains constant.

Step 3: Analyzing Rotational Inertia

When the man extends his arms, his moment of inertia (\(I\)) increases because the mass distribution is farther from the axis of rotation.

Step 4: Analyzing Angular Velocity

Since angular momentum is conserved and \(I\) increases, the angular velocity (\(\omega\)) must decrease to keep \(L\) constant: \[ L = I \omega \implies \omega = \frac{L}{I} \]

Step 5: Analyzing Rotational Kinetic Energy

Rotational kinetic energy (\(K\)) is given by: \[ K = \frac{1}{2} I \omega^2 \] When \(I\) increases and \(\omega\) decreases, the product \(\frac{1}{2} I \omega^2\) changes. Since \(\omega\) decreases more significantly than \(I\) increases, the overall kinetic energy decreases.