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### Course: AP®︎/College Physics 1>Unit 3

Lesson 5: Centripetal acceleration and centripetal force

# Change in centripetal acceleration from change in linear velocity and radius: Worked examples

A worked example finding the change in centripetal acceleration from the change in linear speed, and an example finding the change in centripetal acceleration from the change in radius.

## Want to join the conversation?

• I understand how to tackle these problems, it's fairly straightforward. However, I started this course (College Phyiscs 1) from the beginning and, no, we did not derive the formulas for centripetal acceleration (whether using linear speed or angular) in previous videos. But I hope I'll see those videos, wherever they are. I really think this particular course needs to be organized better so that we are asked questions that we've actually been prepared for.
• Why the formulas of Centripetal Acceleration for the the Question 1 and 2 different?
• They both lead to the same answer, but the formula you use depend on what information you're missing.
• At , why would you answer the question saying the second centripetal force's magnitude decreases by a factor of nine, instead of saying the second centripetal force's magnitude decreases by a factor of 1/9?
• If you decrease something by a factor of 1/9 you are actually multiplying by 9. 10 devided by 1/9 equals 90. Similar to how 2-(-2) equals 4.
• Couldn't you just set acceleration proportional to v^2 because 1/r is technically a constant therefore it can be taken out cuz this is a ratio problem anyways
• starting with the vector's signification then no explaining the other topics is a little bit exhausting for us..
• according to "a=v^2/r," acceleration is inversely proportional to the radius. but why in the second example when the radius is 2r, acceleration also increases by a factor of 2, rather than decreases?
(1 vote)
• You forgot velocity changes as well.

It's easy to show it.
v₁ = rω
When we have 2r and ω stays constant,
v₂ = 2rω
v₂ = 2v₁

Initially, we have
a₁ = rω²

When we have 2r and ω stays constant,
a꜀ = v² / r
a꜀ = (v₂)² / (2r)
a꜀ = (2rω)² / (2r)
a꜀ = 4(rω)² / (2r)
a꜀ = 2rω²
a꜀ = 2a₁
(1 vote)