The Riddler has put Batman on the edge of a rotating disk that has a period of rotation of 4 seconds. He has attached Robin to an ideal spring that bobs up and down in simple harmonic motion. The rotating disk has a radius of 10 meters, a mass of 120 kg, and a rotational inertia given by I = 1/2MR2 . Consider Batman to be a point particle with a rotational inertia of MR2 . The Riddler tells Batman that the spring constant of the spring Robin is connected to has a value equal to 1/2 times the current year. In order to disarm the bomb, Batman must move to a position on the disk that will match his angular velocity with Robin’s angular frequency. At that position, Batman can access the hidden hatch to the bomb. Then Batman must enter the shut off code which is equal to the numerical value of the mechanical energy of Robin’s oscillation. Batman’s mass is 110 kg. Batman knows Robin’s mass to be 100 kg. Batman can see that Robin’s amplitude of oscillation is 3 m. There are 2π radians in 1 revolution. a. Help Batman determine the angular frequency of oscillation of Robin. b. What is Batman’s initial angular velocity? c. How far must Batman be from the center of the spinning disk so that his angular velocity matches Robin’s angular frequency so he can access the panel to get to the bomb? d. What is the code Batman has to enter to disarm the bomb? (That is, what is Robin’s mechanical energy of oscillation equal to?)
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.
4. The Riddler has put Batman on the edge of a rotating disk that has a period of rotation of 4 seconds. He has attached Robin to an ideal spring that bobs up and down in simple harmonic motion. The rotating disk has a radius of 10 meters, a mass of 120 kg, and a rotational inertia given by I = 1/2MR2 . Consider Batman to be a point particle with a rotational inertia of MR2 . The Riddler tells Batman that the spring constant of the spring Robin is connected to has a value equal to 1/2 times the current year.
In order to disarm the bomb, Batman must move to a position on the disk that will match his
Batman knows Robin’s mass to be 100 kg. Batman can see that Robin’s amplitude of oscillation is 3 m. There are 2π radians in 1 revolution.
a. Help Batman determine the angular frequency of oscillation of Robin.
b. What is Batman’s initial angular velocity?
c. How far must Batman be from the center of the spinning disk so that his angular velocity matches Robin’s angular frequency so he can access the panel to get to the bomb?
d. What is the code Batman has to enter to disarm the bomb? (That is, what is Robin’s mechanical energy of oscillation equal to?)
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