How Does the Position on a Turntable Affect a Mass's Acceleration?

[jimbo71]

Homework Statement

A small mass is placed on a record turntable that is rotating at 45 rpm. The acceleration of the mass is
a. greater the farther the mass is from the center
b. greater the closer the mass is to the center
c. independent (in magnitude) of the position of the mass on the turntable
d. directed perpendicular to the line joining the mass and the center of rotation
e. zero

Homework Equations

arad= w^2*r
atan= alpha*r
a= (atan^2+arad^2)^1/2

The Attempt at a Solution

I think the answer is solution A becuase both atan and arad are dependent on the radius of the location of the mass. I am not completely sure this is correct because it seems too easy

 

[Carid]

When I was a child we had roundabouts in public parks. If you sat near the centre it was easy to hang on, but if you moved to the outside you needed all your strength to stay aboard.

 

[thomate1]

.

Your answer is correct. The acceleration of the mass will be greater the farther it is from the center because both the tangential and radial accelerations are dependent on the radius. As the radius increases, the tangential acceleration (atan) will increase, and the radial acceleration (arad) will decrease. This results in a larger overall acceleration for the mass. This is due to the fact that the angular velocity (w) of the turntable is constant, so the tangential acceleration will increase as the radius increases. The radial acceleration, on the other hand, is dependent on the angular acceleration (alpha) which is also constant. Therefore, the farther the mass is from the center, the smaller the radial acceleration will be, resulting in a larger overall acceleration.