**Title: Understanding Angular Motion**The angle that a spinning disc rotates through as a function of time is given in radians as:\[\theta(t) = 2 + 3t - 2t^2\]**a. What is the angular velocity of the disc as a function of time?****b. What is the angular acceleration of the disc?****c. If the disc has a radius of 2 meters, what is the magnitude of the tangential velocity of a point on the edge of the disc when \( t = 10 \) seconds?**---To solve these problems, we need to differentiate the angle function with respect to time:1. **Angular Velocity (\(\omega(t)\)):** \(\omega(t) = \frac{d\theta}{dt} = \frac{d}{dt}(2 + 3t - 2t^2)\).2. **Angular Acceleration (\(\alpha(t)\)):** \(\alpha(t) = \frac{d\omega}{dt} = \frac{d^2\theta}{dt^2}\).3. **Tangential Velocity (\(v_t\)) at the edge with \( r = 2 \) meters when \( t = 10 \)):** Use the formula \(v_t = \omega(t) \times r\).**Graphs and Diagrams Explanation:** There are no graphs or diagrams included in the provided text.

Answered: The angle that a spinning disc rotates…

The angle that a spinning disc rotates through as a function of time is given in radians as 0(t) = 2 + 3t – 2t? a. What is the angular velocity of the disc as a function of time?

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Concept explainers

Angular speed, acceleration and displacement

Angular acceleration is defined as the rate of change in angular velocity with respect to time. It has both magnitude and direction. So, it is a vector quantity.

Angular Position

Before diving into angular position, one should understand the basics of position and its importance along with usage in day-to-day life. When one talks of position, it’s always relative with respect to some other object. For example, position of earth with respect to sun, position of school with respect to house, etc. Angular position is the rotational analogue of linear position.

Question

**Title: Understanding Angular Motion**

The angle that a spinning disc rotates through as a function of time is given in radians as:

\[
\theta(t) = 2 + 3t - 2t^2
\]

**a. What is the angular velocity of the disc as a function of time?**

**b. What is the angular acceleration of the disc?**

**c. If the disc has a radius of 2 meters, what is the magnitude of the tangential velocity of a point on the edge of the disc when \( t = 10 \) seconds?**

---

To solve these problems, we need to differentiate the angle function with respect to time:

1. **Angular Velocity (\(\omega(t)\)):**
\(\omega(t) = \frac{d\theta}{dt} = \frac{d}{dt}(2 + 3t - 2t^2)\).

2. **Angular Acceleration (\(\alpha(t)\)):**
\(\alpha(t) = \frac{d\omega}{dt} = \frac{d^2\theta}{dt^2}\).

3. **Tangential Velocity (\(v_t\)) at the edge with \( r = 2 \) meters when \( t = 10 \)):**
Use the formula \(v_t = \omega(t) \times r\).

**Graphs and Diagrams Explanation:**
There are no graphs or diagrams included in the provided text.

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