A solid wood door 0.900 m wide and 2.20 m high is hinged along one side and has a total mass of 20.0 kg. Initially open and at rest, the door is struck at it center by a blob of mud with a mass 4.00 kg, traveling perpendicular to the door at 12.0 m/s just before impact. The mud sticks to the door after the impact. a. What is the rotational inertia of the door? (Give your answer in kg m2.) I for a plane rotating about its end is: Iplane = 1/3 MR2. b. What is the rotational inertia of the blob of mud about an axis along the
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 solid wood door 0.900 m wide and 2.20 m high is hinged along one side and has a total mass of 20.0 kg. Initially open and at rest, the door is struck at it center by a blob of mud with a mass 4.00 kg, traveling perpendicular to the door at 12.0 m/s just before impact. The mud sticks to the door after the impact.
a. What is the rotational inertia of the door? (Give your answer in kg m2.)
I for a plane rotating about its end is: Iplane = 1/3 MR2.
b. What is the rotational inertia of the blob of mud about an axis along the door's hinge just before the impact? (Give your answer in kg m2.)
The rotational inertia for a point mass is given by: I = mR2.
c. What is the total
d. What is the
e. What is the speed of the doorknob located 0.85 m from the hinge? (Give your answer in m/s.)
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