Centripetal Motion Problems: Solving for Velocity and Acceleration

[helpmeplease8]

Homework Statement

A centripetal-acceleration addict rides in uniform circular motion with period T = 4 s and radius r = 3.00 m. At one instant his acceleration is a = (7.00 m/s2)i + (-3.00 m/s2)j . At that instant, what are the following values?

(a) v·a
(b) r x a

Homework Equations

2∏r/T = speed
v^2/r = acceleration
(4*∏^2*r)/T^2 = acceleration

The Attempt at a Solution

a) (32.97m^2/s^3)i + (-14.13m^2/s^3)j
b) (21m^2/s^2)i + (-9m^2/s^2)j

Are these right?

 

[PhanthomJay]

You don't need to crank out any numbers for the questions asked. In uniform circular motion, acceleration is always inward toward the center, and the instantaneous velocity is tangent to the curved path, perpendicular to the acceleration vector. You are asked to find the dot product of v and a, and the cross product of r and a.

 

[Bhumble]

Welcome to PF.
The dot product is the component of one vector along another. The resulting value is a scalar and will not have directional components (i and j).

The cross product is the resulting vector that is perpendicular to each component involved. The magnitude of this is equal to the parallelogram formed.

The point of this problem is to get you to focus on the directions and operations involved. The numbers aren't that important.