Question 3: Rotational Motion A puck of radius R=4.00cm and mass M=900g is placed on the top of an air table making an angle of o with the horizontal. The puck can rotate freely about the axis passing through its center (its moment of inertia is 1 =MR²). A rope is wrapped around this disk and its second free end is connected to another puck of mass of m = 450g as shown in the figure (g=981 cm/s?). M m The spark timer of the air table starts to operate just after the system is released from rest. The frequency of the spark timer is set to 10 Hz. The table below shows the measurements of position of the disk with mass m: t(s) t2(s?) y(cm) 0.1 0.01 0.7 0.2 0.04 2.7 0.3 0.09 5.8 0.4 0.16 10.5 0.5 0.25 15.9 a) Plot y vs t² graph with proper scaling. b) Draw a best fit line on this graph. Calculate the slope of the best fit line and report the acceleration of the puck with mass m. c) Calculate the angular acceleration of the puck with mass M. d) Calculate sine of the inclination angle of the air table.
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.
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