100% satisfaction guarantee Immediately available after payment Both online and in PDF No strings attached
logo-home
Previously searched by you
Previously searched by you
logo
Summary Circular motion and Gravitation R65,03
Add to cart
Quickly navigate to
Preview
  2.  
  3. University Of Cape Town (UCT)
  4.  
  5. Circular motion and Gravitation (PHY1031F,PHY1023H,PHY1032F)

Summary

Summary Circular motion and Gravitation

 37 views  0 purchase

This is a summary for things you need to know under gravitation and orbital motion. It includes the following: - Important definitions regarding circular motion - Important derivations including centripetal force, tangential velocity, angular velocity, etc... - Universal law of gravitation

Preview 2 out of 5  pages

Document information

  • No
  • Chapter 17 to 18
  • May 6, 2021
  • 5
  • 2020/2021
  • Summary

Subjects

Connected book

book image

Book Title:

Author(s):

  • Edition:
  • ISBN:
  • Edition:

More summaries for

All for this textbook (27)

Written for

All documents for this subject (1)

Seller

avatar-seller
rndmstudent

Content preview

Circular motion & Gravitation- A summary.


• Radian: When arc length is equal to the radial length, the angel subtended at the centre of
the circle is a radian.
• Angular speed (ω): This is the rate of change of angular displacement (θ). It is measured
in rads-1.
• Centripetal force(Fc): Force associated with objects moving in a circular motion; it is
directed towards the centre.



Figure 1




Important formulae and relationships

• Tangential speed(v): The linear speed of an object moving in a circular motion.
𝑣 = 𝜔𝑟




Figure 2




• Centripetal acceleration(a): This is the acceleration caused by an object moving in a
circular motion, it is always directed towards the centre of the circle.
𝑎 = 𝜔2 𝑟
• Period(T): This is the time taken to complete one full rotation, i.e., 360ᵒ or 2π radians
Relationship between vt, ω, and T.

1. v,ω and r

𝑣 = 𝜔𝑟
𝜔 = 𝑣𝑟

, 𝑎 = 𝜔2 𝑟

𝑣2
𝑎= ⋅𝛾
𝑟2
𝑣2
𝑎=
𝑟




2. Fc, a, ω and v
𝐹𝑐 = 𝑚𝑎
𝑎 = 𝜔2 𝑟 𝑜𝑟 𝑎 = 𝜔2 𝑟
𝑚𝑣 2
𝐹𝑐 = 𝑚𝜔2 𝑟 𝑜𝑟 𝐹𝐶 =
𝑟
3. T and ω
2𝜋
𝑇=
𝜔
Gravitation
The universal law of gravitation:
“In the universe, every object attracts every other object with a force that is directly proportional
to the product of the masses of the objects, and indirectly proportional to the square of the
distance between them.”


Figure 3




From the law:
𝐹 ∝ m1 m2
1
𝐹∝
𝑟2
𝑚1 𝑚2
𝐹∝
𝑟2
𝐺𝑚1 𝑚2
𝐹=
𝑟2
Where G is the universal gravitational constant. It has the value: 𝐺 = 6.67 × 10−11 𝑁𝑚2 𝑘𝑔−2 .

The benefits of buying summaries with Stuvia:

Guaranteed quality through customer reviews

Guaranteed quality through customer reviews

Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.

Quick and easy check-out

Quick and easy check-out

You can quickly pay through EFT, credit card or Stuvia-credit for the summaries. There is no membership needed.

Focus on what matters

Focus on what matters

Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!

Frequently asked questions

What do I get when I buy this document?

You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.

Satisfaction guarantee: how does it work?

Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.

Who am I buying this summary from?

Stuvia is a marketplace, so you are not buying this document from us, but from seller rndmstudent. Stuvia facilitates payment to the seller.

Will I be stuck with a subscription?

No, you only buy this summary for R65,03. You're not tied to anything after your purchase.

Can Stuvia be trusted?

4.6 stars on Google & Trustpilot (+1000 reviews)

56326 documents were sold in the last 30 days

Founded in 2010, the go-to place to buy summaries for 14 years now

Start selling
R65,03
  • (0)
Add to cart
Added