When the motion is traveling on a straight line, we say that it travels at a certain linear speed or velocity. But when it is in circular motion, the distance it travels is angular. So, this time, we say that it travels at a certain angular speed or velocity. The relationship between linear velocity and angular velocity is:
V = rω
where
V is the linear velocity
r is the radius of the circle
ω is the angular velocity
The final answer should be in miles per hour. To be consistent, let's transform all distances to miles and time to hour.
Brett's distance:
19 ft + 12 in = 19 ft + 12 in (1 ft/12 in) = 20 ft
1 foot is equal to 0.000189394 mile
20 ft * 0.000189394 = 0.00378788 miles
Will's distance:
12 ft + 3 in = 12 ft + 3(1ft/12in) = 12.25 ft
12.25 ft * 0.000189394 = 0.00232 miles
Next, we convert ω from revolution per minute to radians per minute. One revolution is equal to 2π radians, and 60 minutes is equal to 1 hour:
ω = 2.2 rev/min * (2π rad/1 rev) * (60 min/1 hr)
ω = 264π rad/hour
Now, we can determine the linear velocities of Brett and Will:
Brett's linear velocity = (0.00378788 miles)(264π rad/hour)
Brett's linear velocity = 3.142 miles/h
Will's linear velocity = (0.00232 miles)(264π rad/hour)
Will's linear velocity = 1.924 miles/h
V = rω
where
V is the linear velocity
r is the radius of the circle
ω is the angular velocity
The final answer should be in miles per hour. To be consistent, let's transform all distances to miles and time to hour.
Brett's distance:
19 ft + 12 in = 19 ft + 12 in (1 ft/12 in) = 20 ft
1 foot is equal to 0.000189394 mile
20 ft * 0.000189394 = 0.00378788 miles
Will's distance:
12 ft + 3 in = 12 ft + 3(1ft/12in) = 12.25 ft
12.25 ft * 0.000189394 = 0.00232 miles
Next, we convert ω from revolution per minute to radians per minute. One revolution is equal to 2π radians, and 60 minutes is equal to 1 hour:
ω = 2.2 rev/min * (2π rad/1 rev) * (60 min/1 hr)
ω = 264π rad/hour
Now, we can determine the linear velocities of Brett and Will:
Brett's linear velocity = (0.00378788 miles)(264π rad/hour)
Brett's linear velocity = 3.142 miles/h
Will's linear velocity = (0.00232 miles)(264π rad/hour)
Will's linear velocity = 1.924 miles/h