A compact disc player rated as having speed of 8X will operate at an angular speed of about 4,000 rpm. a) What is the angular speed of the disc in the unit of radian/sec? b) By modelling the compact disc (CD) as a thin uniform disc with mass 10 g, an inner radius of 23 mm, and an outer radius of 58 mm, calculate the rotational inertia of the disc. c) If the torque provided by the motor rotate this disc has the magnitude of
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 compact disc player rated as having speed of 8X will operate at an angular speed of about 4,000 rpm.
a) What is the angular speed of the disc in the unit of radian/sec?
b) By modelling the compact disc (CD) as a thin uniform disc with
mass 10 g, an inner radius of 23 mm, and an outer radius of
58 mm, calculate the rotational inertia of the disc.
c) If the torque provided by the motor rotate this disc has the magnitude of
0.1 N.m. What is the
d) For this angular acceleration, how many radians has the disc rotated, after
2 seconds?
e) How many revolutions in (d) above?
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