Calculating Angular Acceleration of Wheel of Radius R Given Vector of Tot. Acc.

[peripatein]

How may I calculate the angular acceleration of a wheel of radius R given that its vector of total acceleration of a point on its perimeter forms an angle of pi/6 wrt the tangential acceleration at that point at t=1sec after the body has begun its motion?

My attempt at a solution:

a_tot = (-r*w^2,r*dw/dt)
a_tang = (0,r*dw/dt)
Their dot product/product of lengths should yield cosine 30.
I got dw/dt = sqrt(3)w^2

Is that correct? Don't I also know that wt = (pi/2 - pi/6)? Couldn't I have calculated w using that?

 

[tiny-tim]

hi peripatein!

(try using the X² button just above the Reply box )

a_tot = (-r*w^2,r*dw/dt)
a_tang = (0,r*dw/dt)
Their dot product/product of lengths should yield cosine 30.
I got dw/dt = sqrt(3)w^2

yes

but wouldn't it be easier to say that the ratio of the radial and tagential components must be tan30° ?

Don't I also know that wt = (pi/2 - pi/6)?

not following you