Question

Rotating Tray To provide uniform cooking microwave ovens have a glass tray that sits on top of a circular ring with three small wheels, as shown in Figure \(8.36\). When the tray rests on top of the wheels, it is rotated easily by a small motor in the base of the microwave. The rotation of the tray ensures even heating. When the tray completes one full revolution, how many revolutions has the circular ring underneath it completed? Explain.

Short answer

The circular ring completes zero revolutions.

Step-by-step solution

Understand the Mechanism

When the glass tray inside a microwave oven rotates, it sits on three small wheels located on a circular ring. As the tray turns, the wheels make contact with the bottom of the tray, facilitating its movement.

Observe Tray and Ring Movement Relationship

The key to solving this problem is understanding that the circular ring does not actually rotate as the tray revolves. Instead, only the tray is designed to move around its center, maintaining contact with the stationary wheels in the base.

Determine Ring's Revolution Count

Since the wheels move only to facilitate the tray's rotation and do not induce rotation in the ring itself, the circular ring remains static underneath the turning tray. As a result, the circular ring completes zero revolutions when the tray performs one full revolution.

Key concepts

Rotational Mechanics

Rotational mechanics deals with the motion and forces acting on bodies that spin around an axis. In microwaves, rotational mechanics ensure that food is heated evenly. The glass tray in a microwave is a perfect example of these principles in action. As it rotates above a circular ring with wheels, we can observe several key points:

• The tray is the primary object rotating, driven by a motor that applies rotational force.
• The circular ring with wheels remains stationary, only aiding in the smooth rotation of the tray.
• This setup prevents any slipping and ensures that rotation occurs smoothly along a fixed axis.

The glass tray's rotation allows every part of the food to be exposed evenly to microwave radiation, offering consistent cooking outcomes. Understanding this mechanism clarifies why the wheels need only facilitate tray movement without spinning themselves.

Centripetal Force

Centripetal force is the force that keeps an object moving in a circular path. For the glass tray in a microwave, centripetal force comes into play as it rotates. Here’s how it works:

• The motor provides torque to the tray, which induces rotational motion.
• As the tray turns, centripetal force acts inwardly towards the center of rotation, keeping the tray in motion along its circular path.
• The wheels beneath the tray support its weight, but do not interfere with the tray’s movement.

Centripetal force is crucial because it ensures the tray stays on its path and does not slide outward. This force is essential for stable rotation, especially with uneven weight distribution on top. By maintaining a consistent path, the tray allows microwaves to cook food uniformly.

Circular Motion

Circular motion involves any movement where an object follows a circular path. The spinning glass tray inside a microwave oven exhibits circular motion to aid in cooking. Here's a breakdown of how the circular motion of the tray operates:

• The tray rotates steadily around its center, maintaining a constant circular path.
• To achieve circular motion, the tray must have a net force providing constant inward acceleration, which is the centripetal force from the motor.
• The circular ring and its wheels remain fixed, preventing the ring from rotating and diverting any motion to the tray.

Understanding circular motion helps explain why the tray can complete revolutions without the ring moving. The design ensures that the oven doesn’t require complex mechanisms to spin both the tray and the ring, which simplifies functionality. This also protects the internal structure of the microwave from unnecessary wear and tear.