Determine the angular velocity in radians per second of 4.9 revolutions in 5 seconds. use 3.14 for pi.
a) 89 miles per hour
b) 117 miles per hour
c) 149 miles per hour
d) 129 miles per hour

167.08Formula: Angular velocity = 2π * frequency

frequency = 4.9 / 5 seconds = 0.98 / second

Angular velocity = 2π radian * 0.98/sec = 6.1544 radian / sec

To pass it to radian per hour multiply by the factor 3600 sec / hour

=> 6.1544 rad / sec * 3600 sec / hour = 22,155.84 rad/hour.

Now, you have to realize that the answer choices are not angular velocities. They have units of miles per hour, which means that they are linear velocities

To calculate linear velocities you need the radius of the circular path described by the object.

With the radius, then you use the formula V = angular velocity * radius =>

For example if the radius is 0.0402  miles, the linear velocity is 0.00402 miles * 22,155.84/hour = 89 miles per hour

If the radius is 0.00528 miles, V = 0.00528 miles * 22,155.84 / hour = 117 mph

If the radius is 0.00673 miles, V = 0.00673 miles * 22,155.84 / hour = 149 mph

If the radius is 0.00582 miles, V = 0.00582 miles * 22,155.84 / hour = 129 mph.

Now you know how to calculate the angular and linear velocities.