Trig 3.4 Linear and Angular Speed

Front

What is angular speed?

Back

Angular speed is the rate of change of angular position of a rotating object, typically measured in radians per second.

Front

How do you convert revolutions per second to radians per hour?

Back

Multiply the number of revolutions per second by 2π to get radians per second, then multiply by 3600 to convert to radians per hour.

Front

What is the formula for linear speed?

Back

Linear speed (v) can be calculated using the formula v = r * ω, where r is the radius and ω is the angular speed in radians per second.

Front

How do you convert radians to degrees?

Back

To convert radians to degrees, multiply the radian measure by 180/π.

Front

What is the relationship between linear speed and angular speed?

Back

Linear speed is directly proportional to angular speed and the radius of the circular path: v = r * ω.

Front

What is the diameter of a circle if the radius is 14 inches?

Back

The diameter is twice the radius, so the diameter is 28 inches.

Front

If a tire spins at 10 revolutions per second, how many radians does it cover in one second?

Back

In one second, it covers 10 revolutions * 2π radians/revolution = 20π radians.

Front

What is the linear speed of a point on the edge of a circle with a radius of 3 feet rotating at 4 radians per second?

Back

Linear speed v = r * ω = 3 ft * 4 rad/s = 12 ft/s.

Front

What is the angular velocity of a gyroscope rotating at 6 revolutions per second in radians per minute?

Back

Angular velocity = 6 rps * 2π rad/rev * 60 sec/min = 720π rad/min.

Front

What is the linear speed of a ceiling fan with 18 inch blades turning at 5400π radians per hour?

Back

Linear speed = r * ω = 0.75 ft * (5400π rad/hr) = 8100π ft/hr.