A community for students.
Here's the question you clicked on:
 0 viewing
anonymous
 3 years ago
Suppose we are told that the acceleration a of a particle moving with uniform speed v in a circle of radius r is proportional to some power of r, say rn, and some power of v, say vm. Determine the values of n and m and write the simplest form of an equation for the acceleration.
anonymous
 3 years ago
Suppose we are told that the acceleration a of a particle moving with uniform speed v in a circle of radius r is proportional to some power of r, say rn, and some power of v, say vm. Determine the values of n and m and write the simplest form of an equation for the acceleration.

This Question is Open

anonymous
 3 years ago
Best ResponseYou've already chosen the best response.0the value of m and n can be obtained using a tool called dimensional analysis acceleration a has dimension\[L T^{2}\] the velocity has dimension \[LT ^{1}\] and radius of a circle (or any path) is L, the equation of acceleration, can be written \[a = v^{m}r^{n}\]. put the dimensions of a, v, r in the equation respectively yields \[LT ^{2}=\left( LT ^{1} \right)^{m}\left( L \right)^{n}\]. Simplyfing the results, \[LT ^{2}=L^{m+n}T^{m}\]. By comparing the power of L and T on the left hand with the right hand one, we have\[m=2\] and \[m+n=1\]. Substitung m=2 into the last equation,we obtain n=1.And finally we have equation of a in terms of v and r by substituting m and n\[a=v^{m}r ^{n}\] \[a=v ^{2}r ^{1}\] or \[a=\frac{v ^{2} }{ r }\] which is the wellknown centripetal acceleration
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.