Question

На горизонтальном диске, который вращается вокруг неподвижной вертикальной оси с угловой скоростью 10 рад/с, покоится (относительно диска) монета массой 2 г. Если модуль силы взаимодействия монеты с диском 25 мН, то расстояние между центром монеты и осью вращения равно...

Answer 1

W=10 рад/с=2п/Т, Т=2п/10=п/5 с, v=2пR/T =2пR*5/п=10R, Fтяж =mg=2*10^-3*10=20*10^-3 H, тогда по теореме Пифагора Fтяж^2+ F1^2=F^2; F1= корень квадратный из( F^2-maFтяж^2)=корень квадратный из ((25^2-20^2)*10^-6=15*10^-3 Н, mv^2 /R=F1; ,m(10R)^2/R=15*10^-3; 100Rm=15*10^-3; 100*2*10^-3*R=15*10^-3; R=15/200=0,075 м=7,5 см

Answer 2

Calculation of the Distance between the Center of the Coin and the Axis of Rotation

To calculate the distance between the center of the coin and the axis of rotation on a horizontal disk, we can use the concept of torque. Torque is the product of the force applied and the lever arm distance from the axis of rotation.

Given: - Angular velocity of the disk: 10 rad/s - Mass of the coin: 2 g - Force of interaction between the coin and the disk: 25 mN

We can use the equation for torque:

Torque = Force x Distance

The torque acting on the coin is equal to the force of interaction multiplied by the distance between the center of the coin and the axis of rotation.

Let's denote the distance between the center of the coin and the axis of rotation as 'r'. The torque acting on the coin can be written as:

Torque = Force x r

To find the distance 'r', we rearrange the equation:

r = Torque / Force

Now, we can substitute the given values into the equation to find the distance 'r':

r = (25 mN) / (2 g x 10 rad/s)

Converting the units to SI units:

r = (25 x 10^-3 N) / (2 x 10^-3 kg x 10 rad/s)

Simplifying the equation:

r = 1.25 / 2

r = 0.625 meters

Therefore, the distance between the center of the coin and the axis of rotation is 0.625 meters.

Please note that the calculation assumes a uniform disk and neglects any other forces or factors that may affect the system.