Question

Диск закрепленный на горизонтальной оси может вращаться без трения. Масса диска 20 кг. Радиус 1 м. Начальная угловая скорость 0 рад/с По касательной на обод колеса действует постоянная сила 50Н.Какова будет угловая скорость колеса через 20 с.

Answer 1

Объяснение:

оскільки по дотичній на колесо діє сила,то ця сила змінюватиме кутовий імпульс диска

отже можна записати так:

М∆t=∆L

М-момент сили,що діє на диск

М=F*R

∆L=I*∆w ; I=mR²/2

FR∆t=mR²/2*∆w

∆w=2F∆t/mR

∆w=w

отже w=(2F∆t/(mR))

w=20 рад/с

Answer 2

Calculation of Angular Velocity

To calculate the angular velocity of the wheel after 20 seconds, we can use the principle of conservation of angular momentum. The initial angular momentum of the wheel is equal to the final angular momentum.

The formula for angular momentum is given by:

L = Iω

Where: - L is the angular momentum - I is the moment of inertia - ω is the angular velocity

The moment of inertia of a disk rotating about its axis is given by:

I = (1/2) * m * r^2

Where: - m is the mass of the disk - r is the radius of the disk

Given: - Mass of the disk (m) = 20 kg - Radius of the disk (r) = 1 m - Initial angular velocity (ω) = 0 rad/s

We can calculate the moment of inertia (I) using the given values:

I = (1/2) * 20 kg * (1 m)^2 = 10 kg*m^2

Now, we can rearrange the formula for angular momentum to solve for the final angular velocity (ω):

L = Iω

ω = L / I

The angular momentum (L) can be calculated by multiplying the force acting tangentially on the wheel by the radius of the wheel:

L = F * r

Given: - Force acting tangentially on the wheel (F) = 50 N - Radius of the wheel (r) = 1 m

We can calculate the angular momentum (L):

L = 50 N * 1 m = 50 N*m

Now, we can substitute the values of L and I into the formula for ω:

ω = 50 N*m / 10 kg*m^2 = 5 rad/s

Therefore, the angular velocity of the wheel after 20 seconds will be 5 rad/s.