Question

Тело движется по окружности радиусом 20 см. Период обращения = 9,28с. Найти линейную и угловую скорости, ускорения тела.

Answer 1

Во вложении................................

Answer 2

Given Information:

- Radius of the circle: 20 cm - Period of revolution: 9.28 s

Linear Velocity:

The linear velocity of an object moving in a circle is given by the formula:

v = 2πr / T

where: - v is the linear velocity - r is the radius of the circle - T is the period of revolution

Substituting the given values:

v = 2π(20 cm) / 9.28 s

To calculate the linear velocity, we need to convert the radius from centimeters to meters:

v = 2π(0.2 m) / 9.28 s

Simplifying the equation:

v ≈ 0.135 m/s Therefore, the linear velocity of the object is approximately 0.135 m/s.

Angular Velocity:

The angular velocity of an object moving in a circle is given by the formula:

ω = 2π / T

where: - ω is the angular velocity - T is the period of revolution

Substituting the given value:

ω = 2π / 9.28 s

Simplifying the equation:

ω ≈ 0.677 rad/s Therefore, the angular velocity of the object is approximately 0.677 rad/s.

Linear Acceleration:

The linear acceleration of an object moving in a circle is given by the formula:

a = v^2 / r

where: - a is the linear acceleration - v is the linear velocity - r is the radius of the circle

Substituting the given values:

a = (0.135 m/s)^2 / 0.2 m

Simplifying the equation:

a ≈ 0.091 m/s^2 Therefore, the linear acceleration of the object is approximately 0.091 m/s^2.

Angular Acceleration:

The angular acceleration of an object moving in a circle is given by the formula:

α = ω^2 / r

where: - α is the angular acceleration - ω is the angular velocity - r is the radius of the circle

Substituting the given values:

α = (0.677 rad/s)^2 / 0.2 m

Simplifying the equation:

α ≈ 2.29 rad/s^2 Therefore, the angular acceleration of the object is approximately 2.29 rad/s^2.

To summarize: - Linear velocity: 0.135 m/s - Angular velocity: 0.677 rad/s - Linear acceleration: 0.091 m/s^2 - Angular acceleration: 2.29 rad/s^2