Скачать или смотреть Calculate Angular Velocity and Linear Velocity (Part 1)

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The angular velocity, ω, of an object moving along a circular path is the amount of rotation in radians of the object per unit of time and is given by ω=θ/t .

The linear velocity, v, of an object moving along a circular path is the distance traveled by the object, s, per unit of time, t, and is given by v=s/t .

→ Note that s=rθ, where θ is given in radians and r is the radius.

Relationship between Linear Velocity and Angular Velocity

If is the angular velocity of an object moving along a circular path of radius r, then the linear velocity, v, is given by v=rω.

Q1. Determine the angular velocity and the linear velocity of a point on the equator of the Earth. Assume that the radius of the Earth at the equator is 3963 miles.

Q2. The propeller of a small airplane is rotating 1500 revolutions per minute. Find the angular velocity of the propeller in radians per minute.


Q3. In 2008, the old Ferris wheel at the world-famous Santa Monica pier in Santa Monica, California, was replaced with a new solar-powered Ferris wheel that contains thousands of energy-efficient LED (light-emitting diode) lights that can illuminate into many different colors and designs. The wheel is approximately 85 feet in diameter and rotates 2.5 revolutions per minute. Find the linear velocity (in mph) of this new Ferris wheel at the outer edge. Round to two decimal places.

Q4. The propeller of a small airplane is rotating 1500 revolutions per minute. If the propeller blade is 2.5 meters in diameter, find the linear velocity in meters per minute for a point located on the tip of the propeller.


Source: Algebra & Trigonometry, 2e. Trigsted.