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

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

The Attempt at a Solution

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

 

[Doc Al]

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

 

[blob84]

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

 

[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.

 

[asteriatic]

Your attempt at a solution is partially correct. The tangential acceleration can be calculated using the equation a_t = (v_f - v_i)/t, as you have correctly done. However, the radial acceleration cannot be calculated using the given information. It requires knowledge of the angular velocity of the turntable, which is not provided in the problem statement.

The total acceleration can be calculated using the Pythagorean theorem as a = √(a_t^2 + a_c^2). Therefore, the total acceleration at t = 1.25s is a = √(0.4^2 + 1.25^2) = 1.30 m/s^2.

Additionally, it is important to note that the direction of the radial acceleration is always towards the center of the circle, while the direction of the tangential acceleration is tangent to the circle at the given point. In this case, since the point is accelerating from rest towards the final speed, the direction of the tangential acceleration is in the same direction as the final velocity. Therefore, the total acceleration vector would be pointing towards the upper right quadrant of the circle.