(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A small object with mass 3.90 kg moves counterclockwise with constant speed 5.40 m/s in a circle of radius 5.00 m centered at the origin. It starts at the point with position vector (5.00i + 0 j) m. Then it undergoes an angular displacement of 8.00 rad.

(a) What it its position vector?

(b) In what quadrant is the particle located and what angle does its position vector make with the positive x-axis?

(c) What is its velocity? (in components)

(d) In what direction is it moving? (clockwise/anti?)

(e) What is its acceleration? (also in components)

(f) What total force is exerted on the object? (again in components)

2. Relevant equations

a=v^2/r

F=ma

s=θr

v=ωr

a=αr

3. The attempt at a solution

a) Find the position

<-0.739, 4.94>

b) Which quadrant and angle?

Quadrant 2, 98.5 degrees from the horizontal.

c) Velocity?

This is the one I'm having trouble with. First of all, would that 5.40 m/s be angular? If it was angular I would have to multiply it by the radius (5 meters) and find its components. If it's already linear, I would just find the components of that? I don't understand how angular velocity can have components though. Is it like acceleration where one component is towards the center of the circle and the other component is tangent to it?

d) Direction? (Clockwise/Anti)

I think it is going anti-clockwise.

e) Both components of acceleration?

The acceleration would be given by a=v^2/r, but again I don't get how to break this up into its components.

f) Total force on object? (In components)

After I get components of acceleration I'm assuming I can just apply F=ma in both directions separately and get this answer?

Any help would be appreciated.

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# Basic angular motion problem

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