A ladybug of mass m crawls with constant speed v1 (relative to the wheel) along a radial spoke of a bicycle wheel of radius R. The wheel is on a bicycle that is accelerating in the forward direction at a0. At time t0 the bicycle has forward speed v2. Use a coordinate system that has its origin at the center of the wheel, and that rotates with the wheel. At time t0 the ladybug is a distance r from the center of the wheel and the spoke is oriented vertically upward. a) Find all the fictitious forces acting on the ladybug at time t0. b) What is the net force the ladybug must exert on the spoke to continue her journey? (Don’t forget to take gravity into account! Give your answer in vector form, using the rotating coordinate system.)
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 ladybug of mass m crawls with constant speed v1 (relative to the wheel) along a
radial spoke of a bicycle wheel of radius R. The wheel is on a bicycle that is accelerating
in the forward direction at a0. At time t0 the bicycle has forward speed v2. Use a
coordinate system that has its origin at the center of the wheel, and that rotates with the
wheel. At time t0 the ladybug is a distance r from the center of the wheel and the spoke is
oriented vertically upward.
a) Find all the fictitious forces acting on the ladybug at time t0.
b) What is the net force the ladybug must exert on the spoke to continue her journey?
(Don’t forget to take gravity into account! Give your answer in vector form, using the
rotating coordinate system.)
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