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Presentation of physics College of Applied Business Bsc. CSIT 1st semester
An ice skater is spinning with both arms and a leg outstretched. She pulls her arms and a leg inward and her spinning motion changes dramatically. State and derive the useful principle to explain how and why her spinning motion changes? The system of the ice skater does not have any net external torque applied to her. Therefore the angular momentum is conserved for her system. By pulling her arm inward, she reduces the moment of inertia (Smr2) and thus in order to keep the angular momentum the same, her angular speed has to increase.
Principle of conservation of angular momentum: "When the net external torque acting on a system about a given axis is zero , the total angular momentum of the system about that axis remains constant."
Proof: We know that the torque acting on a system is equal to the rate of change of angular momentum of a system about an axis, If no external torque acts on a system, On integrating, we get In general, This .
Moment Of Inertia A quantity expressing a body's tendency to resist angular acceleration, which is the sum of the products of the mass of each particle in the body with the square of its distance from the axis of rotation. It an also be defined as the second moment of mass with respect to distance from an axis. mathematically,
Torque Torque is the measure of how much the force acting on an object causes the object to rotate. The object rotates about an axis which we call pivot point. It is also defined as product of force and a perpendicular distance. = r x F = r F sin()
Relation between torque and moment of inertia A rigid body of mass m rotating about an x-axis with an angular velocity are constituent particles of a rigid body are at distances respectively from the axis of rotation O. The moment of inertia of a body is, Torque will produce a constant angular acceleration in each particle, the magnitude of linear acceleration of particle is given as, And torque of a body,
Some of the examples : • When you twist a bottle lid to open or close it. As well as while opening or closing water flow on tap. • When you spin a top by pulling on a thread in swift motion. • While opening or closing of door.
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