Radian Measure

Front

What is the definition of a radian?

Back

A radian is the angle subtended at the center of a circle by an arc whose length is equal to the radius of the circle.

Front

How many radians are in a full circle?

Back

There are 2π radians in a full circle.

Front

Convert 180 degrees to radians.

Back

180 degrees is equal to π radians.

Front

What is the formula for arc length in a circle?

Back

Arc length (s) = rθ, where r is the radius and θ is the angle in radians.

Front

If the radius of a circle is 5 cm, what is the arc length for an angle of π/3 radians?

Back

Arc length = 5 * (π/3) = 5π/3 cm.

Front

Convert π/4 radians to degrees.

Back

π/4 radians is equal to 45 degrees.

Front

What is the relationship between linear velocity and angular velocity?

Back

Linear velocity (v) = r * ω, where r is the radius and ω is the angular velocity in radians per second.

Front

If a wheel rotates at 60 revolutions per minute, what is its angular velocity in radians per second?

Back

Angular velocity = 60 * 2π / 60 = 2π radians/second.

Front

What is the formula to convert degrees to radians?

Back

Radians = Degrees × (π/180).

Front

Find the arc length of a circle with a radius of 10 inches and an angle of π/2 radians.

Back

Arc length = 10 * (π/2) = 5π inches.