Question

A 35 kg child moves with uniform circular motion while riding a horse on a carousel. The horse is 3.2 m from the carousel's axis of rotation and has a tangential speed of 2.6 m/s.
What is the child's centripetal acceleration?
a.
3.9 m/s2
c.
-2.1 m/s2
b.
2.1 m/s2
d.
1.2 m/s2

Answer 1

Hello!

The answer is:

b. $\frac{2.11m}{s^{2}}$

Why?

The centripetal acceleration or radial acceleration is present when an object is moving to describe a circular path. The centripetal acceleration is always perpendicular to the direction of the velocity and going inwards and towards the center.

The centripetal acceleration can be calculated using the following equation:

$CentripetalAcceleration=\frac{v^{2}}{RadiusOfMotion}$

From the statement we know that:

$v=TangentialSpeed=\frac{2.6m}{s} \\R=3.2m$

So, calculating we have:

$CentripetalAcceleration=\frac{{2.6^{2} \frac{m}{s} }}{3.2m}=\frac{{6.76\frac{m}{s} }}{3.2m}=\frac{2.11m}{s^{2} }$

So, the correct answer is:

b. $\frac{2.11m}{s^{2}}$

Have a nice day!