When bicycle and motorcycle riders ‘pop a wheelie’, a large acceleration causes the bike’s front wheel to leave the ground. Let be the total mass of the bike-plus-rider system; let and be the horizontal and vertical distance of this system’s centre of mass from the rear wheel’s point of contact with ground, as shown in the figure below. (a) Determine the horizontal acceleration a required to barely lift the bike’s front wheel off of the ground. (b) To minimize the acceleration necessary to pop a wheelie, where should be made as small or as large as possible? How about ? How should a rider position his or her body on the bike in order to achieve these optimal values for x and y ? (c) If x = 35cm and y = 95cm , find a.
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.
When bicycle and motorcycle riders ‘pop a wheelie’, a large acceleration causes the bike’s front wheel to leave the ground. Let be the total mass of the bike-plus-rider system; let and be the horizontal and vertical distance of this system’s centre of mass from the rear wheel’s point of contact with ground, as shown in the figure below. (a) Determine the horizontal acceleration a required to barely lift the bike’s front wheel off of the ground. (b) To minimize the acceleration necessary to pop a wheelie, where should be made as small or as large as possible? How about ? How should a rider position his or her body on the bike in order to achieve these optimal values for x and y ? (c) If x = 35cm and y = 95cm , find a.
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