10TH GRADE · KINEMATICS

Free fall and circular motion

Fall without resistance and kinematics of uniform rotation.

24 minutes20 theory cards

LESSON MATERIAL

Basic Concepts

Free fall

The movement of a body is only under the influence of gravity without taking into account the resistance of the environment.

If air resistance can be neglected, the mass of the body does not affect the acceleration of the fall: all bodies move with the same g.

Uniform movement around a circle

Circular motion with a constant speed module.

The magnitude of the velocity is constant, but its direction is constantly changing, so the body has an acceleration towards the center of the circle.

LESSON MATERIAL

Physical quantities

Acceleration of free fall

g

Acceleration of a body in free fall near the surface of a celestial body.

Unit: meters per second squared · $\frac{\mathrm{m}}{\mathrm{s}^2}$

Maximum height

H

The greatest height of body lifting.

Unit: meter · $\mathrm{m}$

Radius

R

The distance from the center of a circle to its point.

Unit: meter · $\mathrm{m}$

Circulation period

T

Time for one full revolution.

Unit: second · $\mathrm{s}$

Frequency

\nu

The number of complete revolutions per unit of time.

Unit: hertz · $\mathrm{Gts}$

Angular velocity

\omega

The speed of changing the angle of rotation.

Unit: radians per second · $\frac{\mathrm{rad}}{\mathrm{s}}$

Rotation angle

\varphi

The angle by which the radius of the body is rotated.

Unit: radian · $\mathrm{rad}$

Centripetal acceleration

a_{\text{ts}}

Acceleration directed towards the center of the circle.

Unit: meters per second squared · $\frac{\mathrm{m}}{\mathrm{s}^2}$

LESSON MATERIAL

Lesson formulas

Free fall speed

v=gt

The speed of a body released without an initial speed increases in proportion to time.

Fall height over time

h=\frac{gt^2}{2}

The height of free fall from rest is determined by time and acceleration.

Maximum lift height

H=\frac{v_0^2}{2g}

The maximum vertical throw height is determined by the initial speed.

Speed through altitude

v=\sqrt{2gh}

The speed of free fall from rest is determined by the height traveled.

Time to fall through altitude

t=\sqrt{\frac{2h}{g}}

The time it takes to fall freely from rest is determined by altitude.

Linear speed around a circle

v=\frac{2\pi R}{T}=2\pi R\nu

In one period the body travels the length of a circle.

Relationship between linear and angular velocities

v=\omega R

Linear speed equals angular speed times radius.

Angular velocity

\omega=\frac{\varphi}{t}=2\pi\nu

Angular velocity is equal to the angle of rotation per time and two pi times the frequency.

Centripetal acceleration via speed

a_{\text{ts}}=\frac{v^2}{R}

Centripetal acceleration increases with the square of the speed and decreases with the radius.

Centripetal acceleration via angular velocity

a_{\text{ts}}=\omega^2R

Centripetal acceleration is equal to the square of the angular velocity times the radius.

Related formulas

PeriodT · with Angular velocityω · rad/s Frequencyν · Hz

PRACTICE

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