Solution to problem 14.2.25 from the collection of Kepe O.E.

14.2.25 The disk rotates with angular velocity? = 8 rad/s. Point M with mass m = 1 kg moves along the radius of the disk according to the law s = 0.2t. Determine the modulus of momentum of this mechanical system at time t = 0.5 s. (0.825)

Problem 14.2.25 is to determine the modulus of momentum of a mechanical system at time t = 0.5 s. To solve the problem it is necessary to know the angular velocity of the disk? and the law of motion of the point M along the radius of the disk s(t).

The disk rotates with angular velocity? = 8 rad/s. The law of motion of point M along the radius of the disk is given by the expression s = 0.2t, where s is the path traveled by point M along the radius of the disk in time t.

To determine the momentum of the system, we use the formula p = mv, where p is the momentum, m is the mass of the body, v is the speed of the body.

The speed of point M can be found as the time derivative of the path: v = ds/dt. To do this, we find the derivative of the function s(t): ds/dt = 0.2.

Now we can calculate the speed of point M at time t = 0.5 s: v = ds/dt * t = 0.2 * 0.5 = 0.1 m/s.

The mass of point M is 1 kg. Then the momentum of the system is p = mv = 1 * 0.1 = 0.1 kg m/s.

Thus, the modulus of momentum of the mechanical system at time t = 0.5 s is equal to 0.1 kg m/s.

Solution to problem 14.2.25 from the collection of Kepe O.?.

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Solution to problem 14.2.25 from the collection of Kepe O.?. consists in determining the modulus of momentum of a mechanical system at time t = 0.5 s.

The disk rotates with angular velocity? = 8 rad/s, and point M with mass m = 1 kg moves along the radius of the disk according to the law s = 0.2t.

To solve the problem, it is necessary to calculate the speed of movement of point M at time t = 0.5 s, using the law of motion s = 0.2t.

s = 0,2t s(0,5) = 0,2 * 0,5 = 0,1 м

Then you should determine the linear speed v of point M:

v = ω * r

where ω is the angular velocity of the disk, r is the radius of the disk.

r = s(0.5) = 0.1 m ω = 8 rad/s

Then

v = 8 * 0.1 = 0.8 m/s

Finally, the modulus of momentum of the system is determined by the formula:

p = m * v

where m is the mass of point M.

m = 1 kg

Then

p = 1 * 0.8 = 0.8 kg m/s

Thus, the modulus of momentum of the mechanical system at time t = 0.5 s is equal to 0.8 kg m/s.

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