ib physics topic 6 & 10 (with some electric fields stuff too) that i found useful to think but the last one didn't help me so this one's probably garbage too

wow this problem is really hard how do i do it?

1. list out all the variables you were given 2. figure out what variables you're trying to find (keep in mind that what you're trying to find might be a different variable in different equations - like k might be the spring constant in some equations or it might denote the coulomb constant. know your stuff ig.) 3. find equations that have those variables. 3a. if those equations have extra variables you weren't explicitly given, see if there's a way to find them (ex: "starts from rest" means u (initial velocity) = 0) 3b. sometimes you might need to set equations equal to each other. (ex: electron in a magnetic field undergoing circular motion means you can set F=qvB equal to F=(mv^2)/r to get qvB=(mv^2)/r. 4. solve. :)

required string tension in circular motion

T=(mv^2)/r

centripetal force

a force that acts on a body moving in a circular path and is directed toward the centre around which the body is moving F=(mv^2)/r=m(w^2)r (data book)

circular motion

any motion in which an object is moving along a curved path - acceleration & force always directed towards the centre (so they are always changing direction - if that's hard for you to understand i get it, just think hard)

tension force

mg +/- ma if the acceleration is opposite the direction of gravity then you add them if it's in the same direction you subtract

angular velocity

rate of change of angular displacement - variable: w (the curly one) w=(change in theta)/time

resultant gravitational field

set gravitational laws equal

Charon is a moon of Pluto that has a mass equal to 1/9 that of Pluto. The distance between the centre of Pluto and the centre of Charon is d. X is the point at which the resultant gravitational field due to Pluto and Charon is zero. What is the distance of X from the centre of Pluto?

set gravitational laws equal. Mc=mass of Charon Mp=mass of Pluto (G*Mc*m)/r^2=(G*Mp*m)/(d-r)^2 G & m cancel, and we know Mc=(1/9)Mp -> Mc/Mp=1/9 *r=distance from point X to Charon's centre so our equation becomes: Mc/r^2=Mp/(d-r)^2 -> Mc/Mp=1/9=(r^2)/((d-r)^2) flipping top and bottom of both sides to make this easier for me personally: 9=((d-r)^2)/(r^2) 3=(d-r)/r 3r=d-r 4r=d d/4 = r d-(d/4)=3d/4