1) What's the linear velocity of a point on the tip of a 6-ft propeller turning at 1200 revolutions per min?
2) A gear is driven by a chain that travels 90m/min. Find the radius of the gear if it makes 50 revolutions per minute.
To find the linear velocity of a point on the tip of a propeller or the radius of a gear, we can use the formula:
Linear velocity = 2 * π * radius * revolutions per minute
1) For the propeller, we are given that it is 6 ft in length and turning at 1200 revolutions per minute. To find the linear velocity, we need to convert the length from feet to the appropriate unit of length. Let's use meters for consistency:
Length of propeller = 6 ft = 6 * 0.3048 m = 1.8288 m
Revolutions per minute = 1200
Now, we can plug these values into the formula:
Linear velocity = 2 * π * 1.8288 m * 1200 rev/min = 13791.85 m/min
Therefore, the linear velocity of a point on the tip of the 6-ft propeller turning at 1200 revolutions per minute is approximately 13791.85 m/min.
2) For the gear, we are given that the chain travels at 90 m/min and the gear makes 50 revolutions per minute. To find the radius of the gear, we rearrange the formula:
Radius = Linear velocity / (2 * π * revolutions per minute)
Plugging in the given values:
Linear velocity = 90 m/min
Revolutions per minute = 50
Radius = 90 m/min / (2 * π * 50 rev/min) = 0.2864 m
Therefore, the radius of the gear is approximately 0.2864 meters.
To calculate the linear velocity of a point on the tip of a propeller, we can use the formula:
Linear velocity = 2πr × Number of revolutions per minute
1) Given:
Radius (r) = 6 ft
Number of revolutions per minute = 1200
Using the formula, we can calculate the linear velocity as follows:
Linear velocity = 2π × 6 ft × 1200 rev/min
Linear velocity = 2π × 6 ft × 1200/1 min
Linear velocity = 2π × 6 ft × 1200/1 min
Linear velocity = 14400π ft/min
Therefore, the linear velocity of a point on the tip of a 6-ft propeller turning at 1200 revolutions per minute is 14400π ft/min.
To find the radius of a gear when given the chain's speed and the gear's revolutions per minute, we can use the following formula:
Linear velocity = 2πr × Number of revolutions per minute
2) Given:
Linear velocity = 90 m/min
Number of revolutions per minute = 50
Using the formula mentioned, we can find the radius as follows:
90 m/min = 2πr × 50 rev/min
90 m/min = 100πr
Dividing both sides of the equation by 100π, we get:
r = 90 m/min / (100π rev/min)
r ≈ 0.286 m
Therefore, the radius of the gear is approximately 0.286 meters.