SCOTT. You can watch the rocket." (a) Find the torque acting on the pole. Ignore the force of gravity on Chris Brown. (i.e. only consider the rocket) (b) Assume that Chris Brown acts like a point mass at one end of the pole and assume he is at the end of the pole. Find the moment of inertia of the system. (c) Find the angular acceleration of the system. (d) Find the amount of time it takes to rotate 90° (π/2 radians). Remember that our formulas are all in radians.
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.
Dr. Evil has captured Chris Brown (m = 65.0 kg)! He threatens to kill him unless the world gives him one milli--- one hundred million dollars. He places Chris Brown on the end of a long, thin pole of mass M = 1000 kg and length L = 5.00 m that is suspended above a pool full of sharks with freaking lasers. The pole is allowed to rotate about its center of mass. A single rocket of negligible mass is placed at the opposite side from Chris Brown. It applies a force of 20.0 N perpendicularly to the pole. When the pole rotates 90°, the singer will fall down into the water.
Watching this for a moment, Dr. Evil is very disappointed at how slowly it is moving.
"SCOTT!" he yells.
Scott: "Yeah?"
"Why is there only one tiny rocket on the end of that pole?"
Scott "We ran out of money buying the sharks with lasers attached to them because we--"
Dr. Evil holds up a forestalling hand. "I'm going to go grab a pizza--NOT YOU SCOTT. You can watch the rocket."
(a) Find the torque acting on the pole. Ignore the force of gravity on Chris Brown. (i.e. only consider the rocket)
(b) Assume that Chris Brown acts like a point mass at one end of the pole and assume he is at the end of the pole. Find the moment of inertia of the system.
(c) Find the
(d) Find the amount of time it takes to rotate 90° (π/2 radians). Remember that our formulas are all in radians.
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