A man with a mass of 80 kg runs with a velocity of 3 m/s along a line tangent to a circular platform (m = 160 kg, radius r= 5 m). The platform is initially at rest and it has a moment of inertia equal to 0.5mr2. a) Given that there is a conservation of angular momentum, calculate the angular velocity of the platform once the runner has jumped on. b) Then, he walks in the direction of the centre of the circular platform; determine the new angular velocity when he reaches the centre. Hints: You know how to convert the linear tangential velocity into an angular velocity. Angular velocity, distance and mass give you an angular momentum, for the man. Now part (a) is just an angular collision problem.
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 man with a mass of 80 kg runs with a velocity of 3 m/s along a line tangent to a circular platform (m = 160 kg, radius r= 5 m). The platform is initially at rest and it has a moment of inertia equal to 0.5mr2.
a) Given that there is a conservation of
b) Then, he walks in the direction of the centre of the circular platform; determine the new angular velocity when he reaches the centre.
Hints: You know how to convert the linear tangential velocity into an angular velocity. Angular velocity, distance and mass give you an angular momentum, for the man. Now part (a) is just an angular collision problem.
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