A solid sphere of uniform density has a mass of 2.42 kg and a radius of 0.432 meters. A force of 13.2 Newtons is applied tangentially to the equator of the sphere. If the sphere is free to rotate without friction about an axis perpendicular to the equator to which the 13.2 Newton force is applied, what is the angular acceleration α of the sphere caused by the applied force? It may be useful to bear in mind that the moment of inertia I for a solid sphere of uniform density is I = (2/5)MR^2 where M is the mass of the sphere and R is the radius of the sphere. Also, bear in mind in this case that the torque τ is τ = RF since the force F is applied tangentially to the equator. A. 15.3 rad/s^2 B. 31.5 rad/s^2 C. 50.3 rad/s^2 D. 68.5 rad/s^2
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 solid sphere of uniform density has a mass of 2.42 kg and a radius of 0.432 meters. A force of 13.2 Newtons is applied tangentially to the equator of the sphere. If the sphere is free to rotate without friction about an axis perpendicular to the equator to which the 13.2 Newton force is applied, what is the
A. 15.3 rad/s^2 B. 31.5 rad/s^2 C. 50.3 rad/s^2 D. 68.5 rad/s^2
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