Answer:
T = 0.3658
Explanation:
The expression to use to calculate the period is the following:
T = 2π √I/Mgd (1)
Where:
I: moment of Innertia of pendulum
g: gravity acceleration (9.81 m/s²)
d: distance of the pivot
M: mass of the disk.
Before we do anything, we will find first the moment of Innertia of the pendulum.
This can be calculated with the following expression:
I = 1/2 MR² + Md² (2)
At the moment we don't have the mass of the disk, but we don't need it, we will express I in function of M, and then, it will be canceled with the M of expression (1). Calculating M we have (Remember that the units of radius and distance should be in meter):
I = 1/2 M(0.0235)² + M(0.0175)²
I = (2.76x10^-4)M + (3.06x10^-4)M
I = (5.82x10^-4)M (3)
Now, we will replace this value in equation (1):
T = 2π √(5.82x10^-4)M / (9.81)*(0.0175)M ---> Here M cancels out
T = 2π √(5.82x10^-4) / (9.81)*(0.0175)
T = 2π * 0.0582
T = 0.3658 s
This is the period of the pendulum
