During a very quick stop, a car decelerates at \(6.75 \, \text{m/s}^2\).**(a)** What is the angular acceleration (in \(\text{rad/s}^2\)) of its \(0.250 \, \text{m}\) radius tires, assuming they do not slip on the pavement? (Indicate the direction with the sign of your answer. Assume the tires initially rotated in the positive direction.)- **Answer:** \(-27 \, \text{rad/s}^2\) (Correct)**(b)** How many revolutions do the tires make before coming to rest, given their initial angular velocity is \(92.0 \, \text{rad/s}\)?- **Answer:** (Blank for student input)**(c)** How long (in \(\text{s}\)) does the car take to stop completely?- **Answer:** \(3.407 \, \text{s}\) (Correct)**(d)** What distance (in \(\text{m}\)) does the car travel in this time?- **Answer:** \(78.361 \, \text{m}\) (Incorrect)**(e)** What was the car's initial velocity (in \(\text{m/s}\))? (Indicate the direction with the sign of your answer.)- **Answer:** \(23 \, \text{m/s}\) (Correct)**Explanation:**- **Angular Acceleration:** The value is negative, indicating the car is slowing down. The formula used relates linear acceleration to angular acceleration through the radius of the tires. - **Revolutions:** To find this, the student must calculate using the relationship between angular velocity, angular acceleration, and the number of revolutions.- **Stopping Time:** Solved using the formula for time with constant acceleration given the initial velocity and deceleration rate.- **Distance Traveled:** Typically calculated using the equation relating distance, initial velocity, acceleration, and time. The given answer has a mistake.- **Initial Velocity:** Calculated using the relationship between angular velocity and linear velocity. The positive sign indicates the initial direction.

Given : Deceleration (a) = -6.75 m/s2 Radius (r) = 0.250 m Initial angular velocity (wo) = 92 rad/s(a) Angular acceleration (α) = a/r α = -6.75/0.250 α = -27 rad/s2 -> Answer (b) w2 - wo2 = 2αθ 02 - 922 = 2(-27)θ θ = 922/(2 x 27) θ = 156.74 rad No. of revolutions (N) = θ/(2π) N = 156.74/(2π) N = 25 rev -> Answer(c) w - wo = (α)t Therefore , t = (w - wo)/α t = (0 - 92)/(-27) t = 3.407 s -> Answer (d) x = rθ x = 0.250(156.74) x = 39.2 m -> Answer (e) vo = rwo vo = 0.250(92) vo = 23 m/s -> Answer

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During a very quick stop, a car decelerates at 6.75 m/s. (a) What is the angular acceleration (in rad/s2) of its 0.250 m radius tires, assuming they do not slip on the pavement? (Indicate the direction with the sign of your answer. Assume the tires initially rotated in the positive direction.) -27 v rad/s? (b) How many revolutions do the tires make before coming to rest, given their initial angular velocity is 92.0 rad/s? revolutions (c) How long (in s) does the car take to stop completely? 3.407 (d) What distance (in m) does the car travel in this time? 78.361 X m (e) What was the car's initial velocity (in m/s)? (Indicate the direction with the sign of your answer.) 23 m/s

During a very quick stop, a car decelerates at 6.75 m/s. (a) What is the angular acceleration (in rad/s2) of its 0.250 m radius tires, assuming they do not slip on the pavement? (Indicate the direction with the sign of your answer. Assume the tires initially rotated in the positive direction.) -27 v rad/s? (b) How many revolutions do the tires make before coming to rest, given their initial angular velocity is 92.0 rad/s? revolutions (c) How long (in s) does the car take to stop completely? 3.407 (d) What distance (in m) does the car travel in this time? 78.361 X m (e) What was the car's initial velocity (in m/s)? (Indicate the direction with the sign of your answer.) 23 m/s

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

During a very quick stop, a car decelerates at \(6.75 \, \text{m/s}^2\).

**(a)** What is the angular acceleration (in \(\text{rad/s}^2\)) of its \(0.250 \, \text{m}\) radius tires, assuming they do not slip on the pavement? (Indicate the direction with the sign of your answer. Assume the tires initially rotated in the positive direction.)

- **Answer:** \(-27 \, \text{rad/s}^2\) (Correct)

**(b)** How many revolutions do the tires make before coming to rest, given their initial angular velocity is \(92.0 \, \text{rad/s}\)?

- **Answer:** (Blank for student input)

**(c)** How long (in \(\text{s}\)) does the car take to stop completely?

- **Answer:** \(3.407 \, \text{s}\) (Correct)

**(d)** What distance (in \(\text{m}\)) does the car travel in this time?

- **Answer:** \(78.361 \, \text{m}\) (Incorrect)

**(e)** What was the car's initial velocity (in \(\text{m/s}\))? (Indicate the direction with the sign of your answer.)

- **Answer:** \(23 \, \text{m/s}\) (Correct)

**Explanation:**

- **Angular Acceleration:** The value is negative, indicating the car is slowing down. The formula used relates linear acceleration to angular acceleration through the radius of the tires.

- **Revolutions:** To find this, the student must calculate using the relationship between angular velocity, angular acceleration, and the number of revolutions.

- **Stopping Time:** Solved using the formula for time with constant acceleration given the initial velocity and deceleration rate.

- **Distance Traveled:** Typically calculated using the equation relating distance, initial velocity, acceleration, and time. The given answer has a mistake.

- **Initial Velocity:** Calculated using the relationship between angular velocity and linear velocity. The positive sign indicates the initial direction.

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