# A free fall of a material point

A free fall of a material point is being examined. In order to find the solution of the considered example formulas for an accelerated motion and kinetic and potential energy in the gravitational field are used.

$$v = v_0 + a \cdot t$$
$$s = v_0 \cdot t + \frac{a \cdot t^2}{2}$$
$$E_k = \frac{m \cdot v^2}{2}$$
$$E_p = m \cdot g \cdot h$$

A free fall of a material point

# Physical pendulum

Physical pendulum is built with rigid body. One of rigid body ends is fixed to the ceiling. Rigid body is able to rotate around axis which is placed exactly in place where rigid’s end is fixed. Rotation axis is perpendicular to the plane of drawing. Rigid body has mass m and inertia I. Rigid body length is 2∙l. Note that inertia I is known for axis of rotations. If physical pendulum is in equilibrium position then it is not moving. In equilibrium position gravity force is balanced by rigid body’s reaction force. In a certain moment pendulum was deflected from its equilibrium and was inclined from vertical position by angle α. Pendulum is under gravity field, so gravity force works on it. Remember that physical pendulum is rigid body so gravity force is placed on rigid body’s gravity center C.

# Mathematical pendulum

Mathematical pendulum is built with massless rope with length l. One of rope’s ends is fixed to the ceiling. To the second end of rope is fixed to the material point with mass m. Material point is then hanged to the rope. When mathematical pendulum is in equilibrium material point is not moving. In equilibrium position gravity force is balanced by rope’s tension force. In a certain moment mathematical pendulum was deflected from its equilibrium and was inclined from vertical position by angle α. Mathematical pendulum is under gravity field, so gravity force works on it.