Math Tutoring on Radian Measure and Application
A Radian is based on the radius of a circle. One Radian is the angle created by bending the radius length around the arc of a circle. Because a Radian is based on an actual part of the circle rather than an arbitrary division, it is a much more natural unit of angle measure for upper-level mathematics.
The circumference of a circle is 2π Radians. So it becomes 2π radians = 360 degrees.
In Math Tutoring, to convert radians to degrees, multiply a radian measure by 180°/π and simplify.
The Length Of An Arc on a circle depends on both the angle of rotation and the radius length of the circle. We know that, a Radian is the measure of an angle that cuts off an arc the same length as the radius. So that a half-rotation is π radians, so the length of the half-circle would be π radius length.
On the other hand, the length ‘s’ of the arc intercepted on a circle of radius ‘r’ by a central angle of measure ‘θ’ radians is given by the product of the radius and the radian measure of the angle. So s=rθ.
One of the major application of Radian is the measurement of Angular Velocity. The measure of how fast a central angle is changing is called Angular Velocity, ω. So ω=θ/t. where ‘θ’ is the measure of the central angle at time ‘t’. θ must be in radians and ω(omega) is expressed in radians per unit of time.
We know that the length ‘s’, of an intercepted arc on a circle with radius ‘r’ by a central angle ‘θ’ is given by s=rθ. So the Linear Speed Around a Circle is
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1. What is Radian and how it is measured?
2. Deduce the relation Radian and Degrees.
3. What is Angular Velocity and how it is measured?
4. How is Linear Speed around a Circle measured?
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