Two wheels are rotating in such a way that the rotation of the smaller wheel causes the larger wheel to rotate. The radius of the smaller wheel is 4.4 centimeters and the radius of the larger wheel is 20.9 centimeters. Through how many degrees wil the larger wheel rotate if the smaller one rotates 89 degrees.
89 * 4.4/20.9
To determine how many degrees the larger wheel will rotate, we can use the concept of angular velocity. The ratio of angular velocities between two wheels connected by their radii is equal to the ratio of their radii.
In this case, the radius of the smaller wheel is 4.4 centimeters, and it rotates 89 degrees. Let's call this the smaller wheel's angular displacement.
The radius of the larger wheel is 20.9 centimeters. To find out how many degrees the larger wheel will rotate, we need to find its angular displacement.
We can set up the following proportion:
Angular displacement of smaller wheel / Radius of smaller wheel = Angular displacement of larger wheel / Radius of larger wheel
Plugging in the values we know:
89 degrees / 4.4 cm = x / 20.9 cm
Cross-multiplying and solving for x (the larger wheel's angular displacement):
x = (89 degrees * 20.9 cm) / 4.4 cm
x ≈ 421.34 degrees
Therefore, if the smaller wheel rotates 89 degrees, the larger wheel will rotate approximately 421.34 degrees.
To find the number of degrees the larger wheel will rotate when the smaller one rotates, we can use the concept of the gear ratio. The gear ratio is the ratio of the number of teeth on the smaller gear to the number of teeth on the larger gear.
In this case, the wheels act as gears. The ratio of their radii is the same as the gear ratio. Let's calculate the gear ratio:
Gear Ratio = Radius of Larger Wheel / Radius of Smaller Wheel
Gear Ratio = 20.9 cm / 4.4 cm = 4.75
The gear ratio tells us that for every 1 degree the smaller wheel rotates, the larger wheel will rotate by 4.75 degrees.
Now, we know that the smaller wheel rotates 89 degrees. To find the rotation of the larger wheel, we can multiply the rotation of the smaller wheel by the gear ratio:
Rotation of Larger Wheel = Rotation of Smaller Wheel * Gear Ratio
Rotation of Larger Wheel = 89 degrees * 4.75 = 422.75 degrees
Therefore, the larger wheel will rotate by 422.75 degrees when the smaller wheel rotates 89 degrees.