A spherical asteroid with radius r = 123 m and mass M = 2.40×1010 kg rotates about an axis at four revolutions per day. A "tug" spaceship attaches itself to a vehicle which follows the asteroid's south pole (as defined by the axis of rotation) and fires its engine, applying a force tangentially to the asteroid's surface keeping the direction of the force in the same plane. The initial situation is shown in the figure. (Figure 1). If F = 265 N, how long will it take the tug to rotate the asteroid's axis of rotation through an angle of 12.0 ∘ by this method?
Angular Momentum
The momentum of an object is given by multiplying its mass and velocity. Momentum is a property of any object that moves with mass. The only difference between angular momentum and linear momentum is that angular momentum deals with moving or spinning objects. A moving particle's linear momentum can be thought of as a measure of its linear motion. The force is proportional to the rate of change of linear momentum. Angular momentum is always directly proportional to mass. In rotational motion, the concept of angular momentum is often used. Since it is a conserved quantity—the total angular momentum of a closed system remains constant—it is a significant quantity in physics. To understand the concept of angular momentum first we need to understand a rigid body and its movement, a position vector that is used to specify the position of particles in space. A rigid body possesses motion it may be linear or rotational. Rotational motion plays important role in angular momentum.
Moment of a Force
The idea of moments is an important concept in physics. It arises from the fact that distance often plays an important part in the interaction of, or in determining the impact of forces on bodies. Moments are often described by their order [first, second, or higher order] based on the power to which the distance has to be raised to understand the phenomenon. Of particular note are the second-order moment of mass (Moment of Inertia) and moments of force.
A spherical asteroid with radius r = 123 m and mass M = 2.40×1010 kg rotates about an axis at four revolutions per day. A "tug" spaceship attaches itself to a vehicle which follows the asteroid's south pole (as defined by the axis of rotation) and fires its engine, applying a force tangentially to the asteroid's surface keeping the direction of the force in the same plane. The initial situation is shown in the figure. (Figure 1).
If F = 265 N, how long will it take the tug to rotate the asteroid's axis of rotation through an angle of 12.0 ∘ by this method?
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