Tangential and Radial Acceleration

[blob84]

Homework Statement

A point on a rotating turntable 20.0 cm from the center accelerates from rest to a final speed of 0.700m/s in 1.75s. (a) At
t = 1.25s, find the magnitude and direction of the radial acceleration, (b) the tangential acceleration, and(c) the total acceleration of the point.

Homework Equations

$$a_t=\frac{v_f-v_i}{t}$$
$$a_c=v^2/r$$

The Attempt at a Solution

$$a_t=0.4m/s^2, t=1.25s→a_c=1.25m/s^2$$
I don't know how to find the total accelleration, are the components of the vector $$a^→=(a_c, a_t)=(1.25, 0.5)m/s^2$$??

 

[Doc Al]

Yes. Those are the components of the acceleration. What's the magnitude of that vector?

 

[blob84]

the magnitude of the vector is:
$$sqrt((a_c)^2+(a_t)^2)=sqrt((1.25^2+0.4^2))=1.31m/s^2$$
and the angle should be $$arctan(a_t/a_c)=arctan(0.4/1.25)=17.7°$$.

 

[Doc Al]

Good. (And you caught your typo in your last equation.)

When you give the angle, be sure to specify with respect to what. A diagram helps.