A gyroscope of radius 18 cm rotates 35 times per minute. What is the linear velocity at a point on the edge of the gyroscope?
v=wr=2PIf*r f= 35/60
r=.18
To find the linear velocity at a point on the edge of the gyroscope, you can use the formula:
Linear velocity = Angular velocity × Radius
Where:
- Linear velocity is the velocity of a point on the edge of the gyroscope
- Angular velocity is the number of rotations per unit time (in this case, per minute)
- Radius is the distance from the center of the gyroscope to the point of interest
In this case, the radius of the gyroscope is given as 18 cm, and it rotates 35 times per minute.
First, convert the number of rotations per minute to angular velocity in radians per minute. Since one revolution (360 degrees) is equal to 2π radians, we can use the conversion factor:
1 revolution = 2π radians
So, to convert rotations to radians, multiply the number of rotations by 2π:
Angular velocity in radians per minute = 35 rotations × 2π radians/rotation = 70π radians/minute
Next, substitute the values into the formula:
Linear velocity = Angular velocity × Radius
Linear velocity = 70π radians/minute × 18 cm
Now, you can calculate the linear velocity:
Linear velocity ≈ 70π radians/minute × 18 cm ≈ 1260π cm/minute
Therefore, the linear velocity at a point on the edge of the gyroscope is approximately 1260π cm/minute.