1. Find the area of a sector having a central angle of 60° in a circle of radius 8 inches.

2. Find the perimeter and area of a circular sector whose angle is 3.5 radians if the circumference of the circle is 58 ft.

3. A point on the wheel of radius 10 feet moves with a linear velocity of 40 feet per second. Find the angular velocity of the wheel in radians per second and in RPM

4. Find the speed in radians and in degrees per second of disc revolving at 90 RPM.

5. A belt moving at 60 feet per second drives a pulley at 240 RPM. Find the diameter of the pulley

6. A car's wheel is 3 feet in diameter. Find its angular velocity if the car travels at 60 miles per hour.

Solution Summary

This provides several examples of radian problems, including perimeter and area of sectors, diameter, and velocity.

...Angular frequency ω = 2П/T = 2П/1.9 = 3.3 radians/sec. ... Simple Harmonic Motion and the Reference Circle. ... A of the motion, (b) the angular frequency , (c) the ...

... Arclength (RQ) ie [ Arclength = angle (in radian) x radius ] Eqn (1) can be ... Let r - radius of the circle. - angular velocity of the particle. ...

... but the units must be same ie radians or degrees ... starts at rest and undergoes a constant angular acceleration as it travels in a horizontal circle of radius ...

... by spinning a sample around in a circle with a ... angle rotated denoted by measured in radians Initial and ... and Time taken to reach an angular velocity from is ...

... arm is revolving about O at the constant rate of 2 radians/sec (angular velocity)for the ... of the velocity and acceleration of the slider (red circle) in the ...

... shadow when the angle of the sun is theta radians. ... ω avg = dt dθ π Therefore, angular velocity of the sun ... Since the revolution is of a circle(circular motion ...

...angular displacement of the baseball (in radians) as it ... one could ﬁnd the frequency from angular speed, multiply ... by the perimeter of the circle which gives ...

... the turning the drum through an angle of 402 radians. ... E. Both its angular momentum and its angular velocity remain constant ... then go around in a circle about the ...

... of mass of the coin appears to rotate in a circle with angular velocity same as ... dθ) Or v_T= ωR (as for small angles sin = in radians and cos ...