### Particle Motion in Circular PathA particle is traveling counterclockwise in a circle of radius \( r = 2.00 \, \text{m} \). At some instant in time, the particle is located by the angular coordinate \( \alpha = 24.0^\circ \). The total acceleration has a magnitude of \( a = 20.0 \, \text{m/s}^2 \) and is directed at an angle \( \beta = 20.0^\circ \) with respect to the radial coordinate. Determine the following at this instant. (Express your answer in vector form.)#### Graph Explanation:The provided diagram shows a circle with the particle's position and motion vectors. Key components on the diagram include:- \( \vec{r} \) (position vector) pointing from the origin to the particle's location on the circle.- \( \alpha \) (angular coordinate) which denotes the angular position of the particle.- \( \vec{v} \) (velocity vector) which is tangential to the circle at the particle's location.- \( \vec{a} \) (acceleration vector) making an angle \( \beta \) with the radial direction. The coordinate system used includes:- \( x \) and \( y \) axes forming a Cartesian plane.- The corresponding position, velocity, and acceleration vectors.#### Questions:(a) **Position Vector**\[ \vec{r} = \, \underline{\hspace{1cm}} \, \text{m} \](b) **Velocity**\[ \vec{v} = \, \underline{\hspace{1cm}} \, \text{m/s} \](c) **Total Acceleration**\[ \vec{a} = \, \underline{\hspace{1cm}} \, \text{m/s}^2 \]Provide answers considering the provided parameters and the diagram for vector calculations.

(a) The position vector of the particle at the given instant will be:

A particle is traveling counterclockwise in a circle of radius r = a = 20.0 m/s2 and is directed at an angle B = 20.0° with respect to the radial coordinate. Determine the following at this instant. (Express your answer in vector form.) 2.00 m. At some instant in time, the particle is located by the angular coordinate a = 24.0°, the total acceleration has a magnitude of y B α (a) position vector r = m (b) velocity V = m/s (c) total acceleration a = m/s2

A particle is traveling counterclockwise in a circle of radius r = a = 20.0 m/s2 and is directed at an angle B = 20.0° with respect to the radial coordinate. Determine the following at this instant. (Express your answer in vector form.) 2.00 m. At some instant in time, the particle is located by the angular coordinate a = 24.0°, the total acceleration has a magnitude of y B α (a) position vector r = m (b) velocity V = m/s (c) total acceleration a = m/s2

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)...

See similar textbooks

Related questions

Q: SUBH

A: For uniform circular motion only one acceleration acts on the particle, i. e., centripetal…

Q: A particle travels clockwise around a circular path as shown below. The speed of the particle is…

A: See below

Q: At t;= 4.00 s, the acceleration of a particle moving at constant speed in counterclockwise circular…

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A: Given : a→ (t)= 6t, 3sin(t), cos (2t)v→ (0)=(-5, 3, -1)r→(0) = (1, 2, -1)

Q: A particle is at rest and at x=0 and y=0 at time = 0. The particle then moves in the x-y plane with…

Q: A projectile is shot from the edge of a cliff 115 m above ground level with an initial speed of vo =…

Q: A projectile is fired from the ground with an initial speed v at an angle 0 above the horizontal.…

A: An object thrown obliquely near the Earth's surface moves in a curved path. The object is called a…

Q: A particle is traveling counterclockwise in a circle of radius r = 3.00 m.At some instant in time,…

A: centripetal acceleration is component of acceleration along the radius ac=15cos20 =V2r45cos20 =V2V =…

Q: The position of a dragonfly that is flying parallel to the ground is given as a function of time by…

Q: Car A is traveling on the circular road at the constant speed of VA = 60 km/h. At the instant 80…

Q: At time t = 0, a particle is located at the point (1,3,8). It travels in a straight line to the…

Q: Consider a projectile with an initial velocity vector given by the following. m m i = 20i+ 35 ") %3D…

A: Given: The velocity of the projectile is v=20 m/si^+35 m/sj^. The time interval is 1.5 s.

Q: A rocket starts at rest on a launchpad. At t = 0 the rocket has a constant acceleration of a= 25…

Q: At the moment t=0, a particle is located at the point (1, 2,3). It travels in a straight line to…

Q: acceleration of the wallet?

A: Given: Radius of circle in which purse is placed, is rp=2.20 m Radius of circle in which wallet is…

Q: A particle is traveling in a circular path at constant speed in four positions as shown below. If…

Q: A cat rides a merry-go-round turning with uniform circular motion. At time t1 = 1.70 s, the cat's…

A: At time t1 = 1.70 s Cat's velocity, v1 = (3.90 m/s)î + (2.50 m/s)ĵ At time t2 = 5.30 s Cat's…

Q: A particle moves horizontally in uniform circular motion, over a horizontal xy plane. At one…

A: Given: At one instant, the particle velocity through the point at coordinates (4.00 m, 4.00 m) is…

Q: A golf ball is driven with the initial conditions shown in the figure. If the wind imparts a…

Q: The velocity V of a particle moving in the xy plane is given by 7 = ( 5.50 t - 5.00 7 )î + 9.00 3.…

A: According to question we need to find--- at which time the velocity of the object will be zero?

Q: A particle moves in a circular path according to the clockwise equation θ(t)=π/4+2t+4t2, where θ is…

Q: In the figure, a ball is thrown leftward from the left edge of the roof, at height h above the…

Q: A pursue at radius 2.00 m and a wallet at radius 3.00 m travel in uniform circular motion on the…

A: Given that , pursue at radius (rp)=2m wallet at radius (rw)=3m…

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

### Particle Motion in Circular Path

A particle is traveling counterclockwise in a circle of radius \( r = 2.00 \, \text{m} \). At some instant in time, the particle is located by the angular coordinate \( \alpha = 24.0^\circ \). The total acceleration has a magnitude of \( a = 20.0 \, \text{m/s}^2 \) and is directed at an angle \( \beta = 20.0^\circ \) with respect to the radial coordinate. Determine the following at this instant. (Express your answer in vector form.)

#### Graph Explanation:

The provided diagram shows a circle with the particle's position and motion vectors. Key components on the diagram include:

- \( \vec{r} \) (position vector) pointing from the origin to the particle's location on the circle.
- \( \alpha \) (angular coordinate) which denotes the angular position of the particle.
- \( \vec{v} \) (velocity vector) which is tangential to the circle at the particle's location.
- \( \vec{a} \) (acceleration vector) making an angle \( \beta \) with the radial direction.

The coordinate system used includes:
- \( x \) and \( y \) axes forming a Cartesian plane.
- The corresponding position, velocity, and acceleration vectors.

#### Questions:

(a) **Position Vector**
\[ \vec{r} = \, \underline{\hspace{1cm}} \, \text{m} \]

(b) **Velocity**
\[ \vec{v} = \, \underline{\hspace{1cm}} \, \text{m/s} \]

(c) **Total Acceleration**
\[ \vec{a} = \, \underline{\hspace{1cm}} \, \text{m/s}^2 \]

Provide answers considering the provided parameters and the diagram for vector calculations.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

Step 2

Step 3

Step 4

Step 5

Trending now

This is a popular solution!

Step by step

Solved in 5 steps with 6 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

Angular speed, acceleration and displacement

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.

Similar questions

A snowmobile is originally at the point with position vector 30.5 m at 95.0° counterclockwise from the x-axis, moving with velocity 4.89 m/s at 40.0°. It moves with a constant acceleration 1.72 m/s2 at 200°. After 5.00 s have elapsed, find the following. (Express your answers in vector form.) (a) its velocity vector. (b) its position vector.
Find the position vector for a particle with acceleration, initial velocity, and initial position given below. á(t) = (2t, 4 sin(t), cos(3t)) v(0) = ( – 3, – 5, – 4) - r(0) = (1, 2, 0) 7 (t) =
A marble slides down on a curved path defined by the parabola y = 0.4x2. When it is at point “A” (xA = 2m; yA = 1.6m), the velocity of the marble v = 8m/s and the tangental acceleration due to gravity is dv / dt = 4ms2. Calculate the normal component and the total magnitude of the accelarion of the mable in that instant.
This problem will involve deriving a formula or two for a projectile launched from one height and angle and landing at a different height on Earth. Begin with a projectile launched at angle 0 above horizontal from a height y₁ with initial velocity Vo. The projectile lands at a point with height y₂. These are the given quantities: vo, 0, y₁, y2 and g. Construct formulae for each of the following, as. a function of given quantities the horizontal distance traveled. the maximum height reached. the time taken. the angle of impact. (find the final velocity components first).
You are on a train that is traveling at 3.0 m/s along a level straight track. Very near and parallel to the track is a wall that slopes upward at a 12° angle with the horizontal. As you face the window (0.777 m high, 2.26 m wide) in your compartment, the train is moving to the left, as the drawing indicates. The top edge of the wall first appears at window corner A and eventually disappears at window corner B. How much time, in seconds, passes between appearance and disappearance of the upper edge of the wall? A B A 3.0 m/s 12⁰ B
The figure below shows an object initially at point A traveling in the +x-direction. It turns in a circular path at constant speed until it is traveling in the +y-direction at point C. The quarter-circle arc from A to C is 239 m in length, and the particle moves from A to C in 33.0 s. Point B on the path is 35.0° below the x-axis. O 35.0⁰ magnitude direction C B x (a) What is the speed of the object (in m/s)? m/s (b) What is the magnitude and direction of the acceleration when the object is at point B? (Enter the magnitude in m/s² and the direction in degrees counterclockwise from the +x-axis.) m/s² ° counterclockwise from the +x-axis
Just need help with part B
A particle moves in a circular path at constant speed. The initial location of the particle is (4.24 m, 6.05 m) at t = 4 s. The velocity of the particle at this time is 3.02 m/s 3 (i.e., directed along the positive y-axis). Acceleration at this time is along the +x axis. At t=10.6 s, v is -3.02 m/s i and the acceleration is directed along the +y axis. Find the radius of the circle. For this problem assume the time interval is less than one full period. T Find the x-coordinate of the center of the circle (in meters): Xcenter m = m Question Help: Read