Question

A gyroscope has a 0.5-kg disk that spins at 40 rev/s. The center of mass of the disk is 15 cm from a pivot with a radius of the disk of 10 cm. What is the precession angular velocity?

a) 2.67 rad/s
b) 4.00 rad/s
c) 1.33 rad/s
d) 5.33 rad/s

Answer 1

The precession angular velocity of the gyroscope is 2.67 rad/s.

Step-by-step explanation:

The precession angular velocity of the gyroscope can be calculated using the formula:

precession angular velocity = (mass of the disk * radius of the disk * spinning angular velocity) / (mass of the disk * radius of the disk ^ 2 + moment of inertia of the disk)

Plugging in the given values:

mass of the disk = 0.5 kg, radius of the disk = 10 cm = 0.1 m, spinning angular velocity = 40 rev/s

moment of inertia of the disk can be calculated using the formula: moment of inertia = (1/2) * mass of the disk * radius of the disk ^ 2

Plugging in the given values:

moment of inertia of the disk = (1/2) * 0.5 kg * (0.1 m) ^ 2

Now, we can substitute the values into the formula to calculate the precession angular velocity.

precession angular velocity = (0.5 kg * 0.1 m * 40 rev/s) / (0.5 kg * (0.1 m) ^ 2 + (1/2) * 0.5 kg * (0.1 m) ^ 2)

precession angular velocity = 2.67 rad/s