Question

Notify Me Bookmark

Point A of the circular disk is at the angular position θ = 0 at time t = 0. The disk has angular velocity ω0 = 0.30 rad/s at t = 0 and subsequently experiences a constant angular acceleration a = 2.1 rad/s2. Determine the velocity and acceleration of point A in terms of fixed i and j unit vectors at time t = 1.3 s. Answers: vA = aA =

Point A of the circular disk is at the angular position θ = 0 at time t = 0. The disk has angular velocity ω0 = 0.30 rad/s at t = 0 and subsequently experiences a constant angular acceleration a = 2.1 rad/s2. Determine the velocity and acceleration of point A in terms of fixed i and j unit vectors at time t = 1.3 s. Answers: vA = aA =

Image text
Point A of the circular disk is at the angular position θ = 0 at time t = 0 . The disk has angular velocity ω 0 = 0.30 r a d / s at t = 0 and subsequently experiences a constant angular acceleration a = 2.1 r a d / s 2 . Determine the velocity and acceleration of point A in terms of fixed i and j unit vectors at time t = 1.3 s .
Answers:
v A = 1 i i + i a A = 1 i i + i

Detailed Answer

0 0

Please enter your email here. You will get email when this question is answered by our tutor.

Doubtrix Logo

Problem is not yet solved!

Click on Notify me to get email when question is answered.

Join Doubtrix with 7-days free trial

  • Icon Correct & Verified Answers
  • Icon No AI-Generated Answers
  • Icon Video Solution for Difficult Questions
  • Icon Work With Experts to Reach at Correct Answers
Notify me Login Sign Up

Similar/Related Questions

Point A of the circular disk is at the angular position θ = 0 at time t = 0. The disk has angular velocity ω0 = 0.21 rad/s at t = 0 and subsequently experiences a constant angular acceleration α = 2.3 rad/s2. Determine the velocity and acceleration of point A in terms of fixed i and j unit vectors at time t = 1.1 s. Answers: vA = ( i + j) m/s aA = ( i + j) m/s2
Solution
0 0

The angular velocity of the disk in figure 1 is ω = 4t2 + 3 rad/s, where t is in seconds. (a) (2 points) What is angular velocity and the magnitude of the (linear) velocity of point A on the disk when t = 0.5 s. (b) (3 points) Let θ be the counter-clockwise angle of point A from the horizontal x-axis. The derivative of the angle of A is the angular velocity of A, i. e. dθ dt = ω. Integrate the angular velocity to get an expression for the angle, θ. Use the condition that at t = 0, θ = 0 to solve for the integration constant. (c) (3 points) Differentiate the angular velocity with respect to time to get an expression for the angular acceleration, α(t). (d) (2 points) What is the angular acceleration and the magnitude of the (linear) acceleration of point A at t = 0.5 s. Figure 1: Problem 2
Solution
0 0

A uniform electric field is directed axially in a cylindrical region that includes a rectangular loop of wire with total resistance R. This loop has radially oriented width a and axially oriented length b, and sits tight against the cylinder axis, as shown in (Figure 1). The electric field is zero at time t = 0 and then increases in time according to E→ = ηt2k^, where η is a constant with units of V/(m⋅s2). Figure 1 of 1 Part A What is the magnitude of the displacement current through a circular loop centered on the cylinder axis with radius r ≤ a, at time t ? Express your answer in terms of some or all of the variables R, a, b, r, t, and constants η, ϵ0, μ0, π. Submit Request Answer Part B Use Ampere's law to determine the magnitude of the magnetic field a distance r ≤ a from the cylinder axis at time t. Express your answer in terms of some or all of the variables R, a, b, r, t, and constants η, ϵ0, μ0, π. Part C What is the magnetic flux at time t through the rectangular wire loop? Express your answer in terms of some or all of the variables R, a, b, r, t, and constants η, ϵ0, μ0, π. Submit Request Answer Part D What magnitude of current flows in the wire? Express your answer in terms of some or all of the variables R, a, b, r, t, and constants η, ϵ0, μ0, π. Part E Does the current flow clockwise or counterclockwise from the perspective shown in the figure? clockwise counterclockwise Submit Request AnswerA uniform electric field is directed axially in a cylindrical region that includes a rectangular loop of wire with total resistance R. This loop has radially oriented width a and axially oriented length b, and sits tight against the cylinder axis, as shown in (Figure 1). The electric field is zero at time t = 0 and then increases in time according to E→ = ηt2k^, where η is a constant with units of V/(m⋅s2). Figure 1 of 1 Part A What is the magnitude of the displacement current through a circular loop centered on the cylinder axis with radius r ≤ a, at time t ? Express your answer in terms of some or all of the variables R, a, b, r, t, and constants η, ϵ0, μ0, π. Submit Request Answer Part B Use Ampere's law to determine the magnitude of the magnetic field a distance r ≤ a from the cylinder axis at time t. Express your answer in terms of some or all of the variables R, a, b, r, t, and constants η, ϵ0, μ0, π. Part C What is the magnetic flux at time t through the rectangular wire loop? Express your answer in terms of some or all of the variables R, a, b, r, t, and constants η, ϵ0, μ0, π. Submit Request Answer Part D What magnitude of current flows in the wire? Express your answer in terms of some or all of the variables R, a, b, r, t, and constants η, ϵ0, μ0, π. Part E Does the current flow clockwise or counterclockwise from the perspective shown in the figure? clockwise counterclockwise Submit Request AnswerA uniform electric field is directed axially in a cylindrical region that includes a rectangular loop of wire with total resistance R. This loop has radially oriented width a and axially oriented length b, and sits tight against the cylinder axis, as shown in (Figure 1). The electric field is zero at time t = 0 and then increases in time according to E→ = ηt2k^, where η is a constant with units of V/(m⋅s2). Figure 1 of 1 Part A What is the magnitude of the displacement current through a circular loop centered on the cylinder axis with radius r ≤ a, at time t ? Express your answer in terms of some or all of the variables R, a, b, r, t, and constants η, ϵ0, μ0, π. Submit Request Answer Part B Use Ampere's law to determine the magnitude of the magnetic field a distance r ≤ a from the cylinder axis at time t. Express your answer in terms of some or all of the variables R, a, b, r, t, and constants η, ϵ0, μ0, π. Part C What is the magnetic flux at time t through the rectangular wire loop? Express your answer in terms of some or all of the variables R, a, b, r, t, and constants η, ϵ0, μ0, π. Submit Request Answer Part D What magnitude of current flows in the wire? Express your answer in terms of some or all of the variables R, a, b, r, t, and constants η, ϵ0, μ0, π. Part E Does the current flow clockwise or counterclockwise from the perspective shown in the figure? clockwise counterclockwise Submit Request AnswerA uniform electric field is directed axially in a cylindrical region that includes a rectangular loop of wire with total resistance R. This loop has radially oriented width a and axially oriented length b, and sits tight against the cylinder axis, as shown in (Figure 1). The electric field is zero at time t = 0 and then increases in time according to E→ = ηt2k^, where η is a constant with units of V/(m⋅s2). Figure 1 of 1 Part A What is the magnitude of the displacement current through a circular loop centered on the cylinder axis with radius r ≤ a, at time t ? Express your answer in terms of some or all of the variables R, a, b, r, t, and constants η, ϵ0, μ0, π. Submit Request Answer Part B Use Ampere's law to determine the magnitude of the magnetic field a distance r ≤ a from the cylinder axis at time t. Express your answer in terms of some or all of the variables R, a, b, r, t, and constants η, ϵ0, μ0, π. Part C What is the magnetic flux at time t through the rectangular wire loop? Express your answer in terms of some or all of the variables R, a, b, r, t, and constants η, ϵ0, μ0, π. Submit Request Answer Part D What magnitude of current flows in the wire? Express your answer in terms of some or all of the variables R, a, b, r, t, and constants η, ϵ0, μ0, π. Part E Does the current flow clockwise or counterclockwise from the perspective shown in the figure? clockwise counterclockwise Submit Request Answer
Solution
3 0