Ethan and Rebecca are riding on a merry-go-round. Ethan rides on a horse at the outer rim of the circular platform, twice as far from the center of the circular platform as Rebecca, who rides on an inner horse. (i) When the merry-go-round is rotating at a constant angular speed, what is Ethan’s angular speed? (a) twice Rebecca’s (b) the same as Rebecca’s (c) half of Rebecca’s (d) impossible to determine (ii) When the merry-go-round is rotating at a constant angular speed, describe Ethan’s tangential speed from the same list of choices.
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.
Ethan and Rebecca are riding on a merry-go-round. Ethan rides on a horse at the outer rim of the circular platform, twice as far from the center of the circular platform as Rebecca, who rides on an inner horse. (i) When the merry-go-round is rotating at a constant angular speed, what is Ethan’s angular speed? (a) twice Rebecca’s (b) the same as Rebecca’s (c) half of Rebecca’s (d) impossible to determine (ii) When the merry-go-round is rotating at a constant angular speed, describe Ethan’s tangential speed from the same list of choices.
Let the radius of inner rim of circular platform be R (where Rebecca is riding)
so, the radius of the outer rim of the circular platform is 2R (where Ethan is riding)
let the tangential speed of Rebecca be V1
and the tangential speed of Ethan be V2
par(i)
Now, it is known that for different particles of a rigid body, the angular speed(w) remains the same. So,if the merry-go-round is rotating at a constant angular speed , that implies both Rebecca's and Ethan's angular speed are same.
so, answer to part(i) is (b)the same as Rebecca's
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