Consider the 13.0 kg motorcycle wheel shown in Figure 9.29. Assume it to be approximately an annular ring with an inner radius of R,- 0.280 m and an outer radius of R2 = 0.300 m. The motorcycle is on its center stand, so that the wheel can spin freely. Figure 9,29. (a) If the drive chain exerts a force of 1800 N at a radius of 5.00 cm, what is the angular acceleration of the wheel? x rad/s (b) What is the tangential acceleration of a point on the outer edge of the tire? wW m/s (c) How long, starting from rest, does it take to reach an angular velocity of 80.0 rad/s?
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.
![**Consider the 13.0 kg motorcycle wheel shown in Figure 9.29. Assume it to be approximately an annular ring with an inner radius of \( R_1 = 0.280 \, \text{m} \) and an outer radius of \( R_2 = 0.300 \, \text{m} \). The motorcycle is on its center stand, so that the wheel can spin freely.**
[Illustration of a motorcycle wheel]
**Figure 9.29.**
**(a)** If the drive chain exerts a force of 1800 N at a radius of 5.00 cm, what is the angular acceleration of the wheel?
\[\boxed{\text{rad/s}^2}\]
**(b)** What is the tangential acceleration of a point on the outer edge of the tire?
\[\boxed{\text{m/s}^2}\]
**(c)** How long, starting from rest, does it take to reach an angular velocity of 80.0 rad/s?
**Additional Materials:**
- Explanation of annular rings and their applications in physics.
- Examples of angular acceleration in everyday objects.
- Interactive simulation of motorcycle wheel dynamics.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcca7b3a9-28ae-495e-82df-ff344407dffc%2Fa47ab454-b5c1-4447-bf1a-5f21ea10452f%2Fltivl0b_processed.jpeg&w=3840&q=75)
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