Sphere A, with a mass of m₁ = 3.00 kg and radius of r = 50.0 mm, is initially pushed to the left imparting a linear velocity of v_o 4.00 m/s. The sphere rolls with sliding until time t when it stabilizes and rolls without sliding. The coefficient of sliding friction between the sphere and the floor is µ = 0.250. Assume that the linear and angular acceleration of the sphere is uniformly accelerated before reaching time t. Determine the following: 1.Before reaching time t, determine the magnitudes of the following: a) frictional force between the sphere and the floor b) Linear acceleration of the sphere (at its centroid) c) Angular acceleration of the sphere. 2. Upon reaching time t, determine the magnitudes of the following: a)Time t at which the sphere will start rolling without sliding b)Angular velocity of the sphere at this time t. c)Linear velocity of the sphere at this time t.
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.
Sphere A, with a mass of m₁ = 3.00 kg and radius of r = 50.0 mm, is initially pushed to the left imparting a linear velocity of v_o 4.00 m/s. The sphere rolls with sliding until time t when it stabilizes and rolls without sliding. The coefficient of sliding friction between the sphere and the floor is µ = 0.250. Assume that the linear and
1.Before reaching time t, determine the magnitudes of the following:
a) frictional force between the sphere and the floor b) Linear acceleration of the sphere (at its centroid) c) Angular acceleration of the sphere.
2. Upon reaching time t, determine the magnitudes of the following:
a)Time t at which the sphere will start rolling without sliding
b)
c)Linear velocity of the sphere at this time t.
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