a pendulum bob has a mass of 1 kg.the length of the pendulum is 2m. the bob is pulled to one side to an angle of 10' from the vertical.what is the angular velocity of the pendulum bob?
To find the angular velocity of the pendulum bob, we can use the formula:
angular velocity (ω) = √(g / L)
where g is the acceleration due to gravity and L is the length of the pendulum.
Given:
Mass of the bob (m) = 1 kg
Length of the pendulum (L) = 2 m
Angle from the vertical (θ) = 10 degrees
First, we need to convert the angle from degrees to radians since the formula requires the angle to be in radians. We know that 1 radian is equal to 180/π degrees. Therefore:
θ (in radians) = (10 degrees) × (π/180)
Now, substituting the given values in the formula:
ω = √(g / L) = √(9.8 m/s² / 2 m)
Calculating the square root:
ω = √4.9 m²/s²
Hence, the angular velocity of the pendulum bob is approximately 2.21 rad/s.