Calculate the angular speed of the pedal sprocket ωp and wheel sprocket ωw in radians per second. b)Calculate the linear speed of the outer edge of the pedal sprocket vp, in centimeters per second. c)Calculate the linear speed of the bicycle v, in meters per second, assuming the wheel does not slip across the ground.
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 bicyclist notes that the pedal sprocket has a radius of rp = 9.5 cm while the wheel sprocket has a radius of rw = 4.5 cm. The two sprockets are connected by a chain which rotates without slipping. The bicycle wheel has a radius R = 62 cm. When pedaling the cyclist notes that the pedal rotates at one revolution every t = 1.2 s. When pedaling, the wheel sprocket and the wheel move at the same angular speed.
a)Calculate the angular speed of the pedal sprocket ωp and wheel sprocket ωw in radians per second.
b)Calculate the linear speed of the outer edge of the pedal sprocket vp, in centimeters per second.
c)Calculate the linear speed of the bicycle v, in meters per second, assuming the wheel does not slip across the ground.
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