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### Course: AP®︎/College Physics 1 > Unit 5

Lesson 2: Kinetic energy# Kinetic energy review

Review the key concepts, equations, and skills for kinetic energy. Understand how kinetic energy can't be negative but the change in kinetic energy can be negative.

## Key terms

Term (symbol) | Meaning | |
---|---|---|

Kinetic energy | Energy from translational or rotational motion. SI units of joules ( | |

Translational motion | Linear motion of a rigid body. SI units of | |

Translational kinetic energy ( | Energy due to linear motion of a rigid body. SI units of joules ( |

## Equations

Equation | Symbols | Meaning in words |
---|---|---|

Translational kinetic energy is directly proportional to mass and the square of the magnitude of velocity. | ||

Change in kinetic energy is the difference between the final and initial kinetic energy. |

## Common mistakes and misconceptions

**Kinetic energy can’t be negative, although the change in kinetic energy**Because mass can’t be negative and the square of speed gives a non-negative number, kinetic energy can’t be negative. Either something is moving and has positive kinetic energy, or it is not moving and has zero kinetic energy. If the final speed is less than the initial speed, then the final kinetic energy is less than the initial kinetic energy and can be negative.$\mathrm{\Delta}K$ is negative.$\mathrm{\Delta}K$ **Some people think doubling speed means doubling the energy.**The kinetic energy is proportional to the square of the speed, so doubling the speed increases the kinetic energy by a factor of . However, doubling the speed does double the momentum, which we will cover in the next unit.$4$

## Learn more

For deeper explanations of kinetic energy, see our article on kinetic energy with worked example problems.

To check your understanding and work toward mastering these concepts, check out the exercise on using the kinetic energy equation.

## Want to join the conversation?

- Is energy scalar or vector?(2 votes)
- It can only be a scalar because it doesn
`t matter the direction it`

s going, just the speed.(3 votes)

- how do you solve K=1/2mv^2(3 votes)
- If you are solving for "m" you would use the following formula.

m = (2(K))/(v^2)

If you are solving for "v" you would use this formula.

v = sqrt((2(K))/(m))(3 votes)

- Is energy scalar or vector?(2 votes)
- Do you think energy has a direction? Of course it has a direction it can flow, but given on its own, its a scalar quantity. It only has magnitude.

We can think of this like mass (energy is mass but in a different form). Mass doesn't have direction, but has magnitude, so its a scalar quantity.(1 vote)

- What is rotational kinetic energy?(1 vote)
- consider watching this Khan video for the answer:

https://www.khanacademy.org/science/ap-physics-1/ap-torque-angular-momentum/rotational-kinetic-energy-ap/v/rotational-kinetic-energy(3 votes)

- how to weight and speed effect eachother?(2 votes)
- why can't I get to the quiz(1 vote)
- If kinetic energy is decreased to 25% of its original value, how does the velocity change?(1 vote)
- KE = 1/2 * m * v^2 <==> v = sqrt(2 * KE / m)

v1 = sqrt(2 * KE / m) = sqrt(2) * sqrt(KE / m)

v2 = sqrt(2 * (.25 * KE) / m) = sqrt(1/2) * sqrt(KE / m)

v1 / v2 = sqrt(1/2)/sqrt(2) * sqrt(KE / m)/sqrt(KE / m)

= sqrt(1/4)*1 = 1/2

v1 = 1/2 * v2

When the kinetic energy is 1/4 of the original value, the new velocity is half of the original velocity.(1 vote)

- how does energy not have a direction?(1 vote)
- It indicates the energy something has. It either is something, or nothing. The energy is to the object, and doesn't have an direction because of that.(1 vote)

- I can not figure out the dependency of kinetic energy on frame of reference(1 vote)
- How do you find m like m=... what(1 vote)
- Im presuming you are trying to make m the subject from e=1/2 mv^2...

then it is m=2e/(v^2)(1 vote)