An oversized yo-yo is made from two identical solid disks each of mass M = 1.90 kg and radius R = 10.9 cm The two disks are joined by a solid cylinder of radius r = 4.00 cm and mass m = 1.00 kg as in the figure below. Take the center of the cylinder as the axis of the system, with positive torques directed to the left along this axis. All torques and angular variables are to be calculated around this axis. Light string is wrapped around the cylinder, and the system is then allowed to drop from rest. (a) What is the moment of inertia of the system? Give a symbolic answer. (Use any variable or symbol stated above as necessary. Do not substitute numerical values; use variables only.) I = (b) What torque does gravity exert on
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.
An oversized yo-yo is made from two identical solid disks each of mass M = 1.90 kg and radius R = 10.9 cm The two disks are joined by a solid cylinder of radius r = 4.00 cm and mass m = 1.00 kg as in the figure below. Take the center of the cylinder as the axis of the system, with positive torques directed to the left along this axis. All torques and angular variables are to be calculated around this axis. Light string is wrapped around the cylinder, and the system is then allowed to drop from rest.
(a) What is the moment of inertia of the system? Give a symbolic answer. (Use any variable or symbol stated above as necessary. Do not substitute numerical values; use variables only.)
I =
(b) What torque does gravity exert on the system with respect to the given axis?
N · m
(C) Write an equation for the
| ? | = |
(g) Eliminate ? from the rotational second law with the expression found in part (d) and find a symbolic expression for the acceleration a in terms of m, M, g, r and R.
| a | = |
|
(h) What is the numeric value for the system's acceleration?
m/s2
(i) What is the tension in the string?
N
(j) How long does it take the system to drop 1.17 m from rest?
s
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