Calculating Linear and Centripetal Acceleration for a Car in Rotational Motion

[pb23me]

Homework Statement

At a particular moment in a race, a car moving around a turn with a radius of 50m had an angular speed of .6rad/sec and an angular acceleration of .2rad/sec²
At this particular moment find:
the linear speed
the centripetal acceleration
its total linear acceleration

Homework Equations

w=$$\Delta$$theta/$$\Delta$$t
v_t=rw
alpha=$$\Delta$$w/$$\Delta$$t

The Attempt at a Solution

linearspeed =50*.6=30m/s
linear acceleration would be a_t=r(alpha) so a_t=10m/s²
I don't know how to calculate the centripetal acceleration

 

[turin]

At this particular moment find:
...
the centripetal acceleration
its total linear acceleration
...
linear acceleration would be a_t=r(alpha) so a_t=10m/s²
I don't know how to calculate the centripetal acceleration

You probably have a formula for centripetal acceleration in your book or notes. This is one of those "given" formulas that you learn (on par with F=m.a in freshman physics). Your other problem is, what do you really mean by "linear acceleration"? Acceleration, like velocity, has a magnitude and direction, i.e. it is a vector. As a vector, it can be broken into components and there is some "resultant" or "total" acceleration. Hint: what is the relationship between the "centripetal" direction, and the direction that you have indicated with a subscript "t"? Identify the components of the acceleration in an appropriate coordinate system.

 

[pb23me]

ok so centripetal acceleration=rw²=18m/s²
i know that centripetal acceleration points towards the center of the circle and linear acceleration is tangential to the circle... i don't know what direction to break linear acceleration up into..

 

[pb23me]

well i just looked at the drawing and it seems to indicate that there is an acceleration 45 degrees inward from a_t

 

[pb23me]

10²+18²=424 so total linear acceleration=20.6m/s²