A wheel has a constant angular acceleration of 2.5 rad/s². Starting from rest, it turns through 330 rad.(a) What is its final angular velocity (in rad/s)? (Enter the magnitude.)[Input Box] rad/s(b) How much time elapses (in s) while it turns through the 330 radians?[Input Box] s **Problem Statement:**A wheel rotates at a constant rate of \(4.30 \times 10^3\) revolutions per minute (rev/min).**(a)** What is its angular velocity in radians per second? (Enter the magnitude.)- [ ] rad/s**(b)** Through what angle does it turn in 12 s? Express the solution in radians and degrees.- In radians: [ ] rad- In degrees: [ ] °**Explanation for Students:**- To convert from revolutions per minute to radians per second, use the relation \(1 \text{ rev} = 2\pi \text{ radians}\) and convert minutes to seconds.- For the angle turned through in 12 seconds, use the angular velocity to find the distance traveled in radians, and then convert to degrees using the relation \(1 \text{ radian} = \frac{180}{\pi} \text{ degrees}\).

Given(n): Angular acceleration, α=2.5 rad/s2 Initial angular velocity, ωi=0 Angular displacement,…

A wheel has a constant angular acceleration of 2.5 rad/s2. Starting from rest, it turns through 330 rad. (a) What is its final angular velocity (in rad/s)? (Enter the magnitude.) rad/s (b) How much time elapses (in s) while it turns through the 330 radians?

A wheel has a constant angular acceleration of 2.5 rad/s2. Starting from rest, it turns through 330 rad. (a) What is its final angular velocity (in rad/s)? (Enter the magnitude.) rad/s (b) How much time elapses (in s) while it turns through the 330 radians?

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

A wheel has a constant angular acceleration of 2.5 rad/s². Starting from rest, it turns through 330 rad.

(a) What is its final angular velocity (in rad/s)? (Enter the magnitude.)

[Input Box] rad/s

(b) How much time elapses (in s) while it turns through the 330 radians?

[Input Box] s

**Problem Statement:**

A wheel rotates at a constant rate of \(4.30 \times 10^3\) revolutions per minute (rev/min).

**(a)** What is its angular velocity in radians per second? (Enter the magnitude.)

- [ ] rad/s

**(b)** Through what angle does it turn in 12 s? Express the solution in radians and degrees.

- In radians: [ ] rad
- In degrees: [ ] °

**Explanation for Students:**
- To convert from revolutions per minute to radians per second, use the relation \(1 \text{ rev} = 2\pi \text{ radians}\) and convert minutes to seconds.
- For the angle turned through in 12 seconds, use the angular velocity to find the distance traveled in radians, and then convert to degrees using the relation \(1 \text{ radian} = \frac{180}{\pi} \text{ degrees}\).

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