If it takes 600s for an object to carry out 20 revolutions:

Question

A. What is the period of rotation?

B. What is the velocity if the object is 14 cm from the center of rotation?

C. What is the centripetal force on a 35 g mass spinning 14 cm from the center of rotation?

Answer 1

Hi Meg;

A. What is the period of rotation?

This is the amount of time required for one rotation...

(600 seconds)/(20 revolutions)

(30 seconds)/(1 revolution)

Period of rotation is 30 seconds.
B. What is the velocity if the object is 14 cm from the center of rotation?

The circumference of the rotation is...

(3.14)(2r)

3.14 is, of course, pi.

r is, of course, the radius.

(3.14)(2)(14 cm)

(3.14)(28 cm)

87.92 cm

In round figures, this is 90 cm.

distance=(velocity)(time)

s=vt

90 centimeters=(velocity)(30 seconds)

(90 centimeters)/(30 seconds)=velocity

3 centimeters/second=velocity

C. What is the centripetal force on a 35 g mass spinning 14 cm from the center of rotation?

force=m(v²/r)

force=(35 g)[(3 cm/s)²/(14 cm)]

force=(35 g)[(9 cm²/s²)/(14 cm)]

Let's note that the unit of cm¹ is in the numerator and denominator.  It cancels...

force=(35g)[(9 cm/s²)/(14)]

force=22.5 g-cm/s²