Velocity is a vector quantity because...

How many normal modes of oscillation or natural frequencies does each if the following have: (

Vadim26 [7]

<span>Each of these systems has exactly one degree of freedom and hence only one natural frequency obtained by solving the differential equation describing the respective motions. For the case of the simple pendulum of length L the governing differential equation is d^2x/dt^2 = - gx/L with the natural frequency f = 1/(2π) √(g/L). For the mass-spring system the governing differential equation is m d^2x/dt^2 = - kx (k is the spring constant) with the natural frequency ω = √(k/m). Note that the normal modes are also called resonant modes; the Wikipedia article below solves the problem for a system of two masses and two springs to obtain two normal modes of oscillation.</span>

6 0

4 years ago

The wheel having a mass of 100 kg and a radius of gyration about the z axis of kz=300mm, rests on the smooth horizontal plane.a.

pickupchik [31]

Answer:

a) 20 rad/s

b) 6 m/s

Explanation:

b) Force acting on the wheel is 200 N

mass of the wheel is 100 kg

From Newton's second law of motion, F = m × a

Where F is the net force acting on the body

m is mass of the body

a is the acceleration of the body

By substituting the values we get, a = 2 m/s²

As acceleration is constant, we can use the below formula for calculating the final velocity of the object

v = u + a × t

Where v is the final velocity

u is the initial velocity

a is the acceleration

t is the time taken

u = 0 (∵ it starts from rest)

By substituting the values we get

v = 0 + 2 × 3 = 6 m/s

∴ Speed of center of mass after 3 seconds = 6 m/s

a) As the wheel rotates about z-axis, radius of gyration will be the radius of wheel

∴ Radius of the wheel = 300 mm

Torque acting on the wheel about axis of rotation = 300 mm × 200 N =

60 N·m

Torque = (Moment of inertia) × (angular acceleration)

Assuming that the mass of spokes of the wheel to be negligible,

Moment of inertia of the wheel about axis of rotation = 100 × 300² × $10^{-6}$ = 9 kg·m²

Then,

60 = 9 × (angular acceleration)

∴ angular acceleration ≈ 6·67 rad/s²

As angular acceleration of the wheel is constant, we can use the below formula for calculation of final angular speed

$w_{f}$ = $w_{i}$ + α × t

Where

$w_{f}$ is the final angular velocity

$w_{i}$ is the initial angular velocity

α is the angular acceleration

t is the time taken

$w_{i}$ is 0 (∵ initially it starts from rest)

By substituting the values we get

$w_{f}$ = 6·67 × 3 = 20 rad/s

∴ Angular velocity of the wheel after three seconds = 20 rad/s

3 0

4 years ago

A hoodlum throws a stone vertically downward with an initial speed v0 from the roof of a building, a height h above the ground.

Vaselesa [24]

V2=u2+2as
v2=144+600
v2=744
v=√744

6 0

3 years ago

Consider each of the electric- and magnetic-field orientations given next. In each case, what is the direction of propagation of

vodka [1.7K]

The route of the propagation of the wave in every case are; A) +z route B) +z route C) -y route D) -x route .

vec Ein is the Electrical area vector and vec Bin is the Magnetic area vector, due to the fact the sphere vectors are continually perpendicular to every different the propagation of the wave is perpendicular to the 2 vectors. The route of the propagation of the wave may be observed with the aid of using vec Ein X vec Bin (Cross made from vectors). This also can be achieved with the aid of using the usage of the RIGHT HAND RULE.

Cross product may be observed with the aid of using

i x j = okay and j x i = - okay

j x okay=i and okay x j = - i

okay x i=j and that i x okay = - j

wherein i represents the +x route, j represents the +y route and okay represents the +z route

The RIGHT HAND RULE may be used to demonstrate the move product with the aid of using the usage of the proper hand and pointing the index finger withinside the route of the primary vector and the center finger alongside the second one vector, the move product is withinside the route of the thumb.

A) vec Ein the +xdirection,vec Bin the +ydirection,

Finding the move made from the 2 vectors (i x j = okay) might provide a vector withinside the +z route

B) vec Ein the -y route,vec Bin the +x route

Finding the move made from the 2 vectors (- j x i = okay) might provide a vector withinside the +z route

C) vec Ein the +z route,vec Bin the -x route

Finding the move made from the 2 vectors (okay x - i = - j) might provide a vector withinside the -y route

D) vec Ein the +y route,vec Bin the -z route

Finding the move made from the 2 vectors (j x - okay = - i) might provide a vector withinside the -x route

The complete question is- Consider each of the electric- and magnetic-field orientations given next. In each case, what is the direction of propagation of the wave?A)\vec Ein the +xdirection,\vec Bin the +ydirection.Please Choose+ x direction- x direction+ y direction- y direction+ z direction- z directionB)\vec Ein the -y direction,\vec Bin the +x directionPlease Choose+ x direction- x direction+ y direction- y direction+ z direction- z directionC)\vec Ein the +z direction,\vec Bin the -x direction.Please Choose+ x direction- x direction+ y direction- y direction+ z direction- z directionD)\vec Ein the +y direction,\vec Bin the -z direction.Please Choose+ x direction- x direction+ y direction- y direction+ z direction- z direction.

Learn more about vector here-

brainly.com/question/13966790

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3 0

1 year ago

What will happen to the velocity and momentum of each ball when the small ball hits the heavier large ball?

kap26 [50]

Most of the momentum is transferred to the ball on top. Since the collision in this situation is elastic, momentum is conserved, meaning the momentum of both balls before hitting the floor is equal to the momentum of both balls right after the collision.

7 0

3 years ago