A helicopter has a rotor (radius R0) that rotates with constant angular speed ω. The helicopter...

A helicopter has a rotor (radius R0) that rotates with constant angular speed ω. The helicopter is accelerating vertically with constant acceleration A0, starting from rest. Using cylindrical coordinates
a) Write the position vector of the tip of the rotor as a function of time.
b) Find the velocity vector of the rotor tip as a function of time by taking the derivative of the previous result.
c) Find the acceleration vector of the rotor tip as a function of time.
d) Find an expression for the angle between a and v at time t.
e) Evaluate your expression from part (d) in the limit as t → ∞.

Solutions

Expert Solution

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

A wheel rotates with a constant angular acceleration of 3.0 rad/. If the angular speed of...

A wheel rotates with a constant angular acceleration of 3.0 rad/. If the angular speed of the wheel is 2 rad/s at t = 0, through what angular displacement does the wheel rotate in 2 s? 10 rad. 6 rad. 15 rad. 4 rad. 12 rad. Based on question number 3, through how many revolutions has the wheel turned during this time interval? 4 rev. 3 rev. 1.6 rev. 5 rev. 2 rev. Based on question number 3, what is...

A disk rotates with constant angular acceleration. The initial angular speed of the disk is 2?...

A disk rotates with constant angular acceleration. The initial angular speed of the disk is 2? rad/s. After the disk rotates through 20? radians, the angular speed is 3? rad/s. (a) What is the magnitude of the angular acceleration? rad/s2 (b) How much time did it take for the disk to rotate through 20? radians? s (c) What is the tangential acceleration of a point located at a distance of 3 cm from the center of the disk? m/s2

The vanes of a helicopter has an angular speed of 60r/min. There are three vanes with...

The vanes of a helicopter has an angular speed of 60r/min. There are three vanes with a length of 4.2 m and a width of 0.25m each. The air is at a temperature of 15ºC. Transition takes place at Recr = 3.2 e5 . Calculate the aerodynamic torque required to overcome skin friction.

The merry-go-round rotates counterclockwise with a constant angular speed u. The distance between the horse on...

The merry-go-round rotates counterclockwise with a constant angular speed u. The distance between the horse on the merry-go-round and the rotational center is r. (a) Find the position of the horse x and its velocity v, v(t) = d/dt x(t), as vector-functions of time. (b) Find the acceleration of the horse, a(t) = d^2/dt^2 x(t), as a vector-function of time. What is its direction (in comparison with the direction of x)? Now the same horse has a non-constant angular speed...

A dielectric cylinder of permitivity ε rotates around its axis with angular velocity ω. If it...

A dielectric cylinder of permitivity ε rotates around its axis with angular velocity ω. If it is inside a uniform magnetic field B parallel yo the cylinder's axis, find the polarización charge in the cylinder

A slender rod with a length of 0.280 m rotates with an angular speed of 8.00...

A slender rod with a length of 0.280 m rotates with an angular speed of 8.00 rad/s about an axis through one end and perpendicular to the rod. The plane of rotation of the rod is perpendicular to a uniform magnetic field with a magnitude of 0.620 T . 1)What is the induced emf in the rod? E= V 2)What is the potential difference between its ends? V= 3)Suppose instead the rod rotates at 8.00 rad/srad/s about an axis through...

A student on a piano stool rotates freely with an angular speed of 3.05 rev/s ....

A student on a piano stool rotates freely with an angular speed of 3.05 rev/s . The student holds a 1.25 kg mass in each outstretched arm, 0.749 m from the axis of rotation. The combined moment of inertia of the student and the stool, ignoring the two masses, is 5.53 kg⋅m2 , a value that remains constant. Part A As the student pulls his arms inward, his angular speed increases to 3.65 rev/s . How far are the masses...

A student on a piano stool rotates freely with an angular speed of 3.05 rev/s ....

A student on a piano stool rotates freely with an angular speed of 3.05 rev/s . The student holds a 1.05 kg mass in each outstretched arm, 0.779 m from the axis of rotation. The combined moment of inertia of the student and the stool, ignoring the two masses, is 5.53 kg⋅m2 , a value that remains constant. Calculate the initial kinetic energy of the system. Calculate the final kinetic energy of the system. Please list every steps

A satellite with Mass m is in orbit with a constant radius around the earth r0...

A satellite with Mass m is in orbit with a constant radius around the earth r0 (RE=6370km, Mass ME = 5,98*1024kg) a) Show that the satellite moves with uniform circular motion and calculate the velocity v0 in dependance of G,M E and R E . b) At which height h above the earth's surface is the geostationary orbit found? Which linear velocity does a satellite have at this height? c) Compare this to the linear velocity on earth's surface as...

A uniform solid sphere with Radius R has KE (rotational) at an angular speed of w...

A uniform solid sphere with Radius R has KE (rotational) at an angular speed of w when spinning about an axis through its center. A uniform thin-walled hollow shell of radius 2R has 1/3 KE (rotational) at an angular speed of w when spinning about an axis through its center. If m=M for solid sphere, whats the mass of the hollow sphere?

Subjects