Mass m1 = 5.0 kg is initially held in place on a horizontal surface. It is connected to mass m2 =3.0 kg via a light string over a 1.5-kg pulley. The pulley is a uniform disk with radius 7.5 cm. Mass m1 is released, and the masses and pulley accelerate as a system. Mass m2 accelerates downward at a rate of 1.68 m/s2 (as shown). a) Draw FBD’s for the two masses and the pulley. (Since the pulley adds resistance to the system, the tension in the horizontal and vertical portions of the string is different.) b) Apply Newton’s 2nd law, translational form, to m2. Find the tension in the vertical portion of the string. c) Apply Newton’s 2nd law, rotational form, to the pulley. Find the tension in the horizontal portion of the string. (Ignore any friction in the axle of the pulley.)
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.
Mass m1 = 5.0 kg is initially held in place on a horizontal surface. It is connected to mass m2 =3.0 kg via a light string over a 1.5-kg pulley. The pulley is a uniform disk with radius 7.5 cm. Mass m1 is released, and the masses and pulley accelerate as a system. Mass m2 accelerates downward at a rate of 1.68 m/s2 (as shown).
a) Draw FBD’s for the two masses and the pulley. (Since the pulley adds resistance to the system, the tension in the horizontal and vertical portions of the string is different.)
b) Apply Newton’s 2nd law, translational form, to m2. Find the tension in the vertical portion of the string.
c) Apply Newton’s 2nd law, rotational form, to the pulley. Find the tension in the horizontal portion of the string. (Ignore any friction in the axle of the pulley.)
d) Apply Newton’s 2nd law, translational form, to m1. Find the coefficient of kinetic friction between m1 and the horizontal surface.
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