Find the torque needed to accelerate the object in the figure to an angular velocity of 20 radians per second in 4 seconds if it starts at rest. The object consists of five spheres where r1 is .75 m and r2 is .45 m. The mass of center sphere is 100 kg and the mass of the little spheres around the outside are 30 kg. (hint: begin with finding the acceleration). The moment of inertia of a sphere is 2/5 mr² and the moment of inertia of a point mass traveling in an orbit is mr2. The object should spin around the center of the large sphere. (note: do not use the parallel axis theorem) r1 r2
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.
Trending now
This is a popular solution!
Step by step
Solved in 3 steps