If you start with arc length = radius x arc angle then differentiate twice wrt time you will get this. The sign depends on your conventions. In vectors, ##\vec {a_T}=\vec r\times\ddot{\vec\theta}##.Alexanddros81 said:
Your last result v = 6.26√(cosθ - cos30deg) is correct.Alexanddros81 said:
The initial angle of the pendulum is 30 degrees.
The initial angle of the pendulum affects the amplitude and period of its motion. A larger initial angle will result in a larger amplitude and longer period, while a smaller initial angle will result in a smaller amplitude and shorter period.
The speed of the pendulum is determined by the length of the pendulum, the acceleration due to gravity, and the initial angle. A longer pendulum will have a slower speed, while a shorter pendulum will have a faster speed. The acceleration due to gravity, which is typically 9.8 m/s^2, also affects the speed of the pendulum. Finally, the initial angle also plays a role in determining the speed of the pendulum.
The pendulum's motion will gradually decrease in amplitude due to energy loss from friction. This will result in a decrease in the pendulum's speed and a shorter period. Eventually, the pendulum will come to rest at its equilibrium position.
Yes, the initial angle of the pendulum can be changed after it is released. This will result in a different amplitude and period of motion. However, the energy loss due to friction will still affect the pendulum's motion over time.