Question

A thin hoop with a mass of 5.0 kg rotates about a perpendicular axis through its center. A force F is exerted tangentially to the hoop. If the hoop’s radius is 2.0 m and it is rotating with an angular acceleration of 2.5 rad/s2, calculate the magnitude of F?
a. 35 N
a. 20 N
c. 25 N
d. 8 N

Answer 1

Answer:

c. 25N if I'm right.........

Answer 2

Mass(m) of the thin hoop $\\ = 5kg$

Radius(r) of the thin hoop $\\ = 2m$

Angular acceleration($\alpha$) $\\ =2.5 \frac{m}{s^{2} }$

Linear acceleration= $\\ angular\ acceleration \times radius$

 $\\a= \alpha \times r\\a= 2.5 \times 2\\= 5\frac{m}{s^{2} }$

The tangential force exerted can be given by: $\\ mass \times acceleration$

 $\\ force= 5\times 5\\\\=25 N$

Hence, the correct option will be c. 25 N.