Question

колесо велосипеда имеет радиус 25см.Определите линейную и угловую скорость точек обода колеса,если оно вращается с частотой 4 Гц

Answer 1

Calculation of Linear and Angular Velocity of a Bicycle Wheel

To determine the linear and angular velocity of a bicycle wheel, we need to know the radius of the wheel and the frequency of its rotation.

Given: - Radius of the wheel = 25 cm - Frequency of rotation = 4 Hz

Linear Velocity:

The linear velocity of a point on the rim of a rotating wheel is given by the formula:

Linear Velocity = 2 * π * Radius * Frequency

Substituting the given values into the formula, we can calculate the linear velocity:

Linear Velocity = 2 * π * 25 cm * 4 Hz

To convert the linear velocity to a more commonly used unit, such as meters per second (m/s), we need to convert the centimeters to meters:

Linear Velocity = 2 * π * 0.25 m * 4 Hz

Calculating the linear velocity:

Linear Velocity = 2 * π * 0.25 m * 4 Hz = 8π m/s

Therefore, the linear velocity of a point on the rim of the bicycle wheel is 8π m/s.

Angular Velocity:

The angular velocity of a rotating wheel is given by the formula:

Angular Velocity = 2 * π * Frequency

Substituting the given value into the formula, we can calculate the angular velocity:

Angular Velocity = 2 * π * 4 Hz

Calculating the angular velocity:

Angular Velocity = 2 * π * 4 Hz = 8π rad/s

Therefore, the angular velocity of the bicycle wheel is 8π rad/s.

Please note that the above calculations assume that the wheel is rotating at a constant speed and that there is no slipping between the wheel and the ground.