Some travel mugs taper outward at the bottom so that they have very wide bases. Why does this shape make such a mug particularly stable and keep it from flipping over during the morning commute?

The center of gravity (CoG) is a key concept in understanding stability. Imagine an object, like our travel mug. The CoG is the point where the entire weight of the object seems to be concentrated. For an object to stay balanced, its CoG must be above its base of support. When the CoG is **low**, the object is **more stable**. It is harder to tilt because you'd need to lift or push more of its weight at once.

In practical terms, think of how much easier it is to balance a book flat on your hand versus balancing it on its spine. The same principle applies to our travel mug. A low CoG means you need to apply more force to move it. If the mug tapers outward at the bottom, its mass is closer to the base, and hence, the CoG is lower. This makes it significantly resistant to tipping over.

The base of an object is the region that touches the ground and supports the object. A wide base means that the object has a larger area of contact with the ground, which increases stability. This is because:

- There is more surface area to balance the object.
- The weight is distributed over a bigger area, reducing the pressure on any single point.

For our travel mug, a wide base means that even if it tilts a bit, there is still a large area of contact with the ground before it tips over. It essentially creates a **broadened foundation** for the mug, making it harder to knock over accidentally. You're more likely to knock over a tall, thin cylinder than a wide, squat one. This wide base is particularly useful in dynamic environments, like a moving vehicle during your morning commute. It keeps the mug steady on uneven surfaces.

Resistance to tipping is all about how much an object can withstand external forces without falling. This resistance is heavily influenced by the object's CoG and the width of its base.

- **Low CoG**: A low center of gravity makes it tougher for external forces (like a sudden stop in a car) to cause tipping. The object's weight acts **closer to the ground**.
- **Wide base**: This provides a more substantial area over which external forces must act to tip the object.

Combining these factors, a wide-based, low CoG travel mug resists tipping by needing more force to lift or shift its weight outside its base area. This makes it more resilient to bumps and sudden movements, so you can enjoy your coffee without worrying about spills, especially on your commute.

Overall, by understanding these principles, designers can create products that perform well under real-world conditions, ensuring both functionality and safety.