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

Answer:

Option A is correct.

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

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!!!

Answer 2

Answer:

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

Explanation:

The radial acceleration is equal to:

$a_{c} =\frac{v^{2} }{r}$

If the radial velocity is:

$v=rw$

Replacing:

$a_{c} =\frac{(rw)^{2} }{r} =w^{2} r$

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:

$a_{c,B} >a_{c,A}$