Fear Factor

A spool of radius 100m and mass 100kg has 100 grooves of radii 1m, 2m, ..., 100m. We use pulleys to suspend masses from the grooves as shown. The mass (i)kg is associated with the groove of radius (100-i)m.

Find the angular acceleration of the spool.

So you don't know how to find the Radius of curvature?

Lets try it again.

A particle is projected with a velocity 10m/s at an angle 37* with horizontal. Whats the radius of curvature at t=0? At what instant is the radius of curvature minimum?

Find the radius as a function of time.

Solution: Radius of curvature

F=1i`+2j`+3k`
V=-2i`+3j`-k`

Now, the component of force perpendicular to the velocity is (m*|V|^2)/r.

This component is |F|*Sin(Q)=2*14/r
or sqrt(14)*Sin(Q)=(2*14)/r

or r=(2*sqrt(14))/Sin(Q)

Q is the angle b/w the 2 vectors F and V.

Radius of Curvature

Do you know how we find the radius of curvature of a particle's path?

A force 1i`+2j`+3k` acts on a particle (mass=2) moving with a velocity -2i`+3j`-k`. What is the radius of curvature of the particle's path at this instant?