Fixed Point Rotation Examples

Example 1

The platform centered at O rotates about the z axis at a constant rate of 1 rad/s. The disk with point A rotates at a rate of 3 rad/s. Find the angular velocity and acceleration of the disk with point A, and the velocity and acceleration of point A.

Given: P=1 rad/s, s=3 rad/s as shown, rA=.25 m

Find: , , vA, aA

P=1 rad/s Always in z direction

s=3 rad/s

Example 2

Disk A of the gyroscope spins about its axis, which is inclined at 23.6 relative to the xy-plane, at the constant angular speed of 1=50 rad/s. At the same time, frame B rotates about the z-axis with the variable angular velocity 2. At the instant when 2=20 rad/s and d2/dt=600 rad/s2, find the angular velocity of disk A and the angular acceleration of disk A.

Given: 1=50 rad/s, =23.6, 2=20 rad/s, d2/dt=600 rad/s2

Find: ,

1

2 x

z

y

23.6

A

B

Example 3

The gyroscope has the constant angular velocities shown. Find the angular velocity and angular acceleration of the gyroscope. The angle is 60 at this instant.

Given: s=10 rad/s, p=5 rad/s, n=3 rad/s

Find: ,

s=10 rad/s

p=5 rad/s

n=3 rad/s