Question

Центростремительное ускорение точки, движущейся равномерно по окружности, равно 32 см/с2, диаметр окружности 4 см. Угловая скорость точки равна<br /><br />1)<br /><br />4 рад/с 2) 2 рад/с<br /><br />3)<br /><br />16 рад/с 4) 8 рад/с<br /><br /> можете с решением и с формулой

Answer 1

Омега=v/0.02    v²/0.02=0.32 cm/cek²  v=0.08 m/ cek
омега=0.08/0.02=4 рад/сек   ответ №1

Answer 2

Centripetal Acceleration and Angular Velocity

Centripetal acceleration is the acceleration experienced by an object moving in a circular path. It is directed towards the center of the circle and its magnitude can be calculated using the formula:

a = (v^2) / r

where: - a is the centripetal acceleration - v is the linear velocity of the object - r is the radius of the circular path

In this case, the centripetal acceleration of a point moving uniformly on a circle is given as 32 cm/s^2, and the diameter of the circle is 4 cm. To find the angular velocity of the point, we need to first calculate the radius of the circle.

Calculating the Radius

The diameter of the circle is given as 4 cm. The radius is half the diameter, so:

r = 4 cm / 2 = 2 cm

Calculating the Linear Velocity

To calculate the linear velocity, we can use the formula:

v = ω * r

where: - v is the linear velocity - ω is the angular velocity - r is the radius of the circle

Since we don't have the angular velocity, we need to find it using the given centripetal acceleration.

Finding the Angular Velocity

We can rearrange the formula for centripetal acceleration to solve for the angular velocity:

a = (v^2) / r

Substituting the given values:

32 cm/s^2 = (v^2) / 2 cm

Rearranging the equation:

v^2 = 32 cm/s^2 * 2 cm = 64 cm^2/s^2

Taking the square root of both sides:

v = √(64 cm^2/s^2) = 8 cm/s

Now we can substitute the value of linear velocity into the formula for linear velocity:

8 cm/s = ω * 2 cm

Solving for ω:

ω = 8 cm/s / 2 cm = 4 rad/s

Answer

Therefore, the angular velocity of the point moving uniformly on the circle is 4 rad/s.