A child plays with a yo-yo with an outer radius of 2.9 cm and a mass of 250 g, equipped with a string wound around the central part of the yo-yo on a circle with an inner radius of 1.3 cm (see diagram below). The moment of inertia of the yo-yo is equal to 1.89×10^-4 kg·m^2. After imparting a clockwise angular velocity ω of 25 rad/s to the yo-yo, the child places the yo-yo against a horizontal surface (coefficient of kinetic friction of 0.17) by pulling vertically on the wound string, as illustrated in the diagram below, using a force F of 0.80 N. (The child will maintain the magnitude and orientation of the force F during the yo-yo's movement.) Hint: The kinetic friction force is applied forward since the yo-yo has an angular velocity in the clockwise direction and is not moving (it was initially placed on the surface horizontally). Thus, it can be asserted that the yo-yo initially slides on the horizontal surface (it does not roll without sliding!!!). (a) How much time will elapse before the yo-yo rolls without sliding on the horizontal surface? (This moment corresponds to the situation where the tangential velocity of the yo-yo is related to its angular velocity by (vx = r ω ). (b) How many rotations will the yo-yo complete before it rolls without sliding on the horizontal surface?
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.
The yo-yo
A child plays with a yo-yo with an outer radius of 2.9 cm and a mass of 250 g, equipped with a string wound around the central part of the yo-yo on a circle with an inner radius of 1.3 cm (see diagram below). The moment of inertia of the yo-yo is equal to 1.89×10^-4 kg·m^2.
After imparting a clockwise
Hint: The kinetic friction force is applied forward since the yo-yo has an angular velocity in the clockwise direction and is not moving (it was initially placed on the surface horizontally). Thus, it can be asserted that the yo-yo initially slides on the horizontal surface (it does not roll without sliding!!!).
(a) How much time will elapse before the yo-yo rolls without sliding on the horizontal surface? (This moment corresponds to the situation where the tangential velocity of the yo-yo is related to its angular velocity by (vx = r ω ).
(b) How many rotations will the yo-yo complete before it rolls without sliding on the horizontal surface?
*Diagram of the yo-yo rotating clockwise above a horizontal surface in the image.*
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