Question

A toy airplane is attached to the ceiling by a 46cm long string. The planes flies in a circular path at a constant speed. The propeller turns off and the plane makes a 25 degree angle with the string. It does not move up or down. Predict the period of the plane's motion.

Answer 1

Consider a particle of mass m is suspended from a ceiling through a strong of length L. The particle moves in horizontal circle of radius r.Let the angle made by the string with the vertical be

.

Then,

Here, L =46cm = 0.46m

   = 25°

Therefore, radius of the circle r =

= 0.46 × sin 25

= 0.194 m

We have the equation for velocity v =

=

=0.94 m/s

Angular velocity = velocity ÷ radius

=  

=4.847 rad/s

Also ,

frequency  

= 0.77 /s

Also ,

Therefore time period T =

=

= 1.296 s

= 1.3 s

The period of the plane's motion T = 1.3 s