Answer
Give that,
mass of two student m = 3.10 kg
distance from the axis of the rotation is r = 1 m
angular speed ω = 0.754 rad /s
moment of inertia I = 3.10 kg m²
position from the rotation of the axis is r_1 = 0.29 m
Total moment of inertia I ' = I + 2 m r²
= 3.1 +2 x 3.1 x( 1)^2
= 9.3 kg m²
moment of inertia inward horizontally from the position of rotation axis is
I" = I + 2 m r^2
= 3.1 + 2 * 3.1 kg ( 0.29)^2
= 3.62 kg m^2
a ) new angular speed is ω_1 =
=
= 1.94 rad /s
b ) K.E before the system pulls weight inward is
c )K.E after the system pulls weight inward is
Answer:
The polar coordinate of is .
Explanation:
Given a point in rectangular form, that is , its polar form is defined by:
(1)
Where:
- Norm, measured in meters.
- Direction, measured in sexagesimal degrees.
The norm of the point is determined by Pythagorean Theorem:
(2)
And direction is calculated by following trigonometric relation:
(3)
If we know that and , then the components of coordinates in polar form is:
Since and , direction is located at 3rd Quadrant. Given that tangent function has a period of 180º, we find direction by using this formula:
The polar coordinate of is .
To solve this problem we will apply the kinematic equations of linear movement. For this purpose we will begin to define the final speed of the body before hitting the street. The first equation will begin using the difference in velocities as a function of acceleration (gravity) and position. And the second will use the concept of acceleration, time and speed, to find the time variable.
PART A) Equation of motion is
Replacing,
The speed of rock before hitting the ground is 32.74m/s
PART B) Equation of motion
Therefore the time taken by the rock is 5.58s
Then the speed of the rider is, v = 2m/s
The linear velocity of an object in a straight line is its speed.
The following is the relationship between linear and angular velocity:
v = rω
The circumference of the bicycle wheel is,
2r = 2
r = 0.318m
The angular velocity of the wheel is,
ω = 1rev/sec = 2rad/s
Then the speed of the rider is,
v = rω
v = 0.318×2π
v = 2m/s
Learn more about angular velocity here:
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W = Fd
W = 1225 N x 10 m = 12250