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Chapter 3: Problem 14

An object has kinetic energy, but it stays in one place. What must it be doing?

Short Answer

Expert verified
Answer: An object can have kinetic energy without changing its position if it has rotational kinetic energy, which means it is spinning around an axis in place.

Step by step solution

01

Understanding Kinetic Energy

Kinetic energy is the energy possessed by an object due to its motion. The formula for kinetic energy is given by: \(KE = \frac{1}{2}mv^2\), where \(KE\) is the kinetic energy, \(m\) is the mass of the object, and \(v\) is the object's speed when it's moving or in motion.
02

Introducing Rotational Kinetic Energy

An object can have kinetic energy in two ways: linear motion (like movement from one point to another) and rotational motion (like spinning around an axis). Since the problem states that the object stays in one place, we can consider rotational kinetic energy.
03

Rotational Kinetic Energy Formula

For an object spinning around an axis, the rotational kinetic energy is given by: \(KE_{rot} = \frac{1}{2}Iω^2\), where \(KE_{rot}\) is the rotational kinetic energy, \(I\) is the moment of inertia of the object, and \(ω\) is the angular velocity (how fast the object is spinning).
04

Conclusion

Since the object has kinetic energy but does not change its position, it must be spinning around an axis in place. This implies that the object possesses rotational kinetic energy.

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