Question

Consider a ‘physical pendulum’ made of a meter stick (length L = 1 m, mass 0.2 kg) with a hole drilled through it at the 5 cm mark. The stick is free to rotate (in a vertical plane) around a nail that goes through the hole and into a wall. Assume no friction between the nail and the hole. The stick’s moment of inertia about the nail is I=0.1 kgm². (Use g=10 m/s²)

If the pendulum is released from rest at an angle of 10 degrees away from its resting position, how much time will one full oscillation take? Express your answer in units of seconds, but enter only the numeric answer. Round your answer to 3 decimal places.

Answer 1

we know, time taken for one oscillation is called time period.
so, we need to find the time period of the given physical pendulum.

we know, Time period of physical pendulum, T = 2*pi*sqrt(I_support/(m*g*Lcm))

here
I_support -->moment of inertia about the given axis of rotation
m --> mass of the pendulum
Lcm --> distance from axis of rotation to center of mass.

from the give problem,
I_support = 0.1 kg.m^2
m = 0.2 kg
Lcm = (L/2) - 0.05
= (1/2) - 0.05
= 0.45 m

so,

T = 2*pi*sqrt(0.1/(0.2*10*0.45))

= 2.09 s <<<<<<<<<<-----------------Answer