During the spin cycle the time dependent angular speed of a washing machine drum is given by the equation co(t) = at + b² - cf where a = 2.2 rad/s², b = 0.75 rad/s³ and c = 0.035 rad/s³. At time t=0 s, a point P on the washer drum is located at 60 = 1.9 rad. Zaffiro, MacEe-macee.zaffiro@doane.edu Write an equation for the angular acceleration of the drum, as a function of time, in terms of the given parameters. a(1) = В P 00 789 HOME b с M^^4 5 6 g h || /||* || 1 23 k m 0 END CLEAR t NO BACKSPACE DEL Submit Hint Feedback I give up! What is the angular acceleration, in radians per square second, at time = 3.1 s? Write an equation for the angular position of the point P, as a function of time, in terms of the given parameters. a d j n P
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.
![**Angular Acceleration of a Washing Machine Drum**
During the spin cycle, the time-dependent angular speed of a washing machine drum is given by the equation:
\[ \omega(t) = at + bt^2 - ct^4 \]
where:
- \( a = 2.2 \, \text{rad/s}^2 \)
- \( b = 0.75 \, \text{rad/s}^3 \)
- \( c = 0.035 \, \text{rad/s}^5 \)
At time \( t = 0 \) seconds, a point \( P \) on the washer drum is located at \( \theta_0 = 1.9 \) radians.
### Task 1: Write an equation for the angular acceleration of the drum as a function of time \( t \)
\[ \alpha(t) = \]
Please use the interactive keyboard below to input your equation. The keyboard includes various symbols and letters to help you formulate your response.
**Interactive Keyboard Layout:**
- Symbols and letters: \( \beta, \rho, \theta_0, \alpha, t, \div, \times, ^, \cdot, +, -, \text{BACKSPACE}, \text{CLEAR}, \text{HOME}, \text{END} \)
- Numbers: \( 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 \)
### Task 2: What is the angular acceleration in radians per square second at \( t = 3.1 \) seconds?
### Task 3: Write an equation for the angular position of the point \( P \) as a function of time, in terms of the given parameters.
### Task 4: What is the angular position of the point \( P \) on the drum in radians at \( t = 3.1 \) seconds?
**Note:** Utilize the interactive keypad to submit your answers and request hints if needed.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fae03891c-e92c-4b81-9f2f-8939da4f4f36%2F8fc74c76-c944-49fb-bccc-c13aad4ebec5%2Fnvewi5q_processed.png&w=3840&q=75)
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