- #1
bikerboi92
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Homework Statement
what is the angular displacement after 45 second if a wheel spins at 46.07669 radians/s
Homework Equations
The Attempt at a Solution
i got 2073.45105 and i don't know why that is not right
Is the speed constant? Or does it start from rest? (Unless you post the exact question--word for word--we can only guess if there's something you might have missed.)bikerboi92 said:the wheel makes 22 revolutions in 3 seconds
bikerboi92 said:the wheel makes 22 revolutions in 3 seconds
thats the only other information
nrqed said:[..]Depending on th eprecision they want, the answer they are looking for could be 2070 rad or 2100 rad.
Interesting point! (Which I suppose is what Delphi51 was getting at earlier.)kbaumen said:Wait a minute! Displacement isn't the same as distance.
Doc Al said:Interesting point! (Which I suppose is what Delphi51 was getting at earlier.)
See if they just want the change in angle (mod 2π). (It's worth a shot.)
But I disagree that this is common usage, since angular motion is one dimensional. The parallel kinematic equations would be (for uniformly accelerated motion):
[tex]x = x_0 + v_0t + 1/2 a t^2[/tex] (For linear motion.)
[tex]\theta = \theta_0 + \omega_0t + 1/2 \alpha t^2[/tex] (For rotation.)
Just like x is the linear displacement, so is θ the total angular "displacement" (not mod 2π).
Angular displacement in radians is a measure of the angle through which an object has rotated, expressed in terms of the length of the arc along the circumference of a circle. It is usually denoted by the symbol θ and is measured in radians.
Angular displacement in radians and degrees are two ways of measuring angles. While degrees are based on dividing a circle into 360 equal parts, radians are based on the length of the arc along the circumference of a circle. One radian is equivalent to approximately 57.3 degrees.
To calculate angular displacement in radians, you need to know the initial and final positions of the object, measured in radians. The angular displacement is then given by the difference between these two positions. You can also use the formula Δθ = s/r, where Δθ is the angular displacement, s is the length of the arc, and r is the radius of the circle.
Yes, angular displacement in radians can be negative. This happens when the object rotates in a clockwise direction, which is considered the negative direction. Positive angular displacement occurs when the object rotates in a counterclockwise direction.
Angular displacement in radians is used in many fields, including physics, engineering, and navigation. It is particularly useful for measuring rotational motion, such as the rotation of a wheel or the movement of a pendulum. It is also used in calculating the angular velocity and acceleration of objects. In navigation, it is used to determine the direction and distance of an object based on its angular displacement from a reference point.