Question

Two bugs are riding a turntable whose angular speed is constantly increasing with time. Bug A being closer to the edge and Bug B is farther from the edge of the turntable. Which is true regarding the two bugs' tangential accelerations (in magnitude)?

a.Bug A is experiencing a greater radial acceleration than Bug B.
b.Impossible to answer without knowing the masses of the two bugs.
c.Bug A and Bug B are experiencing the same nonzero radial acceleration.
d.Bug A and Bug B are both experiencing zero radial acceleration.
e.Impossible to answer without knowing the radius of the turntable.
f.Bug B is experiencing a greater radial acceleration than Bug A.

Answer 1

The answer is: f. Bug B is experiencing a greater radial acceleration than Bug A.

Step-by-step explanation:

The radial acceleration is equal to:

`a_(c) =(v^(2) )/(r)`

If the radial velocity is:

`v=rw`

Replacing:

`a_(c) =((rw)^(2) )/(r) =w^(2) r`

According the problem w is the same for both A and B and r is the distance from center, then:

`r_(B) >r_(A)`

According to this expression, it can be concluded that:

`a_(c,B) >a_(c,A)`

Answer 2

Option A is correct.

Bug A is experiencing a greater radial acceleration than Bug B.

Step-by-step explanation:

The two bugs have the same angular speed, w, but different radii of the circular motion.

Bug A is closer to the edge of the turntable and bug B is farther from the edge of the turntable.

Hence, Bug A has a bigger radius of circular motion, hence, its radius can be called R and the radius of the circular motion for bug B is r.

v = wr

The radial acceleration of a body in circular motion is given as

α = (v²/r) = rw²

Radial acceleration for bug A = Rw²

Radial acceleration for bug B = rw²

Since we established that R > r and the angular speeds are equal,

Rw² > rw²

Hope this Helps!!!