Question

A top has moment of inertia 3.2×10−4kg·m2 and radius 4.0 cm from the center of mass to the pivot point. If it spins at 20.0 rev/s and is precessing, how many revolutions does it precess in 10.0 s?

a) 240 revolutions
b) 200 revolutions
c) 160 revolutions
d) 120 revolutions

Answer 1

Without the mass of the top, we cannot directly calculate the precession angular velocity and therefore the number of precessional revolutions. If the precession angular velocity is known, the number of precession revolutions in 10.0 s would be found by dividing the product of precession angular velocity and time by 2π.

Step-by-step explanation:

To calculate the number of precession revolutions that the top makes in 10.0 s, we need to find the precession angular velocity. The precession angular velocity (ωp) is determined by the torque (τ) due to the gravitational force and the angular momentum (L) due to the spinning of the top:

τ = r * m * g * sin(θ)

L = I * ωs

ωp = τ / L

Where:

• r is the distance from the center of mass to the pivot point
• m is the mass of the top
• g is the acceleration due to gravity
• θ is the angle the top's axis makes with the vertical
• I is the moment of inertia of the top
• ωs is the spinning angular velocity

Here, however, the mass (m) of the top is not provided, so we cannot calculate the torque and, subsequently, the precession angular velocity directly. Nevertheless, if we already know the precession angular velocity, we can calculate the number of precessional revolutions as follows:

Number of revolutions = ωp * t / (2 * π), where t is the time in seconds.

The question does not give enough information to determine the precession angular velocity, but if this value were provided or calculated previously, the student could then plug in the numbers to find the total number of revolutions during the 10.0 s interval.