ch 6 rotational motion

1 rad =

180/pi degrees

angle of rotation

change in theta = change in s/r

angular displacement

change in theta = change in s/r

angular velocity

w = change in theta/change in time

linear velocity

w = change in theta/change in time

tangential velocity

v = w*r

instantaneous velocity

v = w*r

angular acceleration

a = change in w/change in time

positive direction in angular acceleration = which direction?

counterclockwise direction

negative direction in angular acceleration = which direction?

clockwise direction

positive angular acceleration = faster or slower? and how does angular velocity change?

faster, increase angular velocity

negative angular acceleration = faster or slower? and how does angular velocity change?

slower, decrease angular velocity

4 rotational motion formular

1. Wf = W0 + at

2. theta = W0*t + 1/2at²

3. W² = Wo² + 2a*theta

4. W = (W0+Wf)/2

angular momentum with units

L = I*w, units: kgm²/s

moment of inertia with units

I = mr², units: kgm²

moment of inertia for hoop about cylinder axis

I = mr²

moment of inertia for solid cylinder/disk about cylinder axis

I = (mr²)/2

moment of inertia for solid sphere around any diameter

I = (2mr²)/5

roatational/translational kinetic energy

KE = W = 1/2*I*w²

Newton second law in two ways

F = ma

tau = I*a = mr²a

centripetal acceleration

a = v²/r

centripetal force

F = ma = m*v²/r

Newton universal law of gravitation

F = GMm/r²

G = 6.673e-11 Nm²/kg²

acceleration due to gravity in terms of gravitational constant, mass, and distance

g = GM/r²

escape velocity

V = sqrt(2Gm/r)