A motorcycle, which has an initial linear speed of 8.9 m/s, decelerates to a speed of 1.3 m/s in 5.4 s. Each wheel has a radius of 0.63 m and is rotating in a counterclockwise (positive) directions. What is (a) the constant angular acceleration (in rad/s²) and (b) the angular displacement (in rad) of each wheel? (a) Number i (0) Units 000
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.
Please help me with the concept of how to work this practice problem out. Thank you
![**Problem Statement:**
A motorcycle, which has an initial linear speed of 8.9 m/s, decelerates to a speed of 1.3 m/s in 5.4 s. Each wheel has a radius of 0.63 m and is rotating in a counterclockwise (positive) direction. What is (a) the constant angular acceleration (in rad/s²) and (b) the angular displacement (in radians) of each wheel?
**Diagram Explanation:**
The diagram shows two motorcycles. The first one is labeled with an initial velocity \( v_0 \) and an initial angular velocity \( \omega_0 \) both pointing to the left (v, the linear speed of the motorcycle, and \(\omega\), the angular speed of the wheels, respectively). The second motorcycle indicates the situation at a later time when the velocity has decreased.
**Questions:**
(a) Number [Input Box] | Units [Dropdown]
(b) Number [Input Box] | Units [Dropdown]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd261088c-f753-45e4-ae14-7adbaf3c257c%2Fed2bfc08-b0ea-48b1-9edb-5fedeb1b9cbb%2F5p5ll8c_processed.png&w=3840&q=75)
Here
Initial linear speed = u = 8.9 m/s
final linear speed = v = 1.3 m/s
time interval for this change = t = 5.4s
radius of wheel = R = 0.63 m 0.63
I have to calculate
a. the angular acceleration.
b. the angular displacement.
Step by step
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