1) Consider a bowling ball of 9.50 kg, a moment of inertia of 2.80E-02 kg·m², and a radius of 0.150 m. If it rolls down the lane without slipping at a linear speed of 7.50 m/s, what is its total kinetic energy? 2) A 2.5 kg mass is moving in a straight line at 12.5 m/s towards the edge of a disk with a diameter of 1.5 m. The angular momentum of the mass, in kg m2/s, is most nearly? 3)A child sits on a carousel at a distance of 8.50 m from the center and rotates through an arc length of 6.50 m. What is the angular displacement of the child? 3) You are attempting to lift a 350 kg sofa to your third-floor apartment building using a pulley system that has a mechanical advantage of 12. Which force must be exerted by you to lift the sofa? 4) An automobile tire with a radius of 0.30 m accelerates from rest at a constant 2.0 rad/s². What is the tangential component of acceleration for a point on the outer edge of the tire? 5)A bucket filled with water has a mass of 23.0 kg and is attached to a rope that is wound around a cylinder with a radius of 0.15 m at the top of a well. What torque does the load produce on the cylinder?
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.
1) Consider a bowling ball of 9.50 kg, a moment of inertia of 2.80E-02 kg·m², and a radius of 0.150 m. If it rolls down the lane without slipping at a linear speed of 7.50 m/s, what is its total kinetic energy?
2) A 2.5 kg mass is moving in a straight line at 12.5 m/s towards the edge of a disk with a diameter of 1.5 m. The
3)A child sits on a carousel at a distance of 8.50 m from the center and rotates through an arc length of 6.50 m. What is the
3) You are attempting to lift a 350 kg sofa to your third-floor apartment building using a pulley system that has a mechanical advantage of 12. Which force must be exerted by you to lift the sofa?
4) An automobile tire with a radius of 0.30 m accelerates from rest at a constant 2.0 rad/s². What is the tangential component of acceleration for a point on the outer edge of the tire?
5)A bucket filled with water has a mass of 23.0 kg and is attached to a rope that is wound around a cylinder with a radius of 0.15 m at the top of a well. What torque does the load produce on the cylinder?
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