Dynamics 109 Kinematics of Bodies – A ring with outer radius r4=2.5in and inner radius r3=2in rolls clockwise without slipping at The center shaft with radius r1=1in rotates counterclockwise at =5radians/s. ωR=10radians/s. ωS Find the angular velocity of the bearings with radius r2=0.5in. There is no slipping at the ωB contact points. Solution: For a wheel that rolls without slipping, there is a simple relation between the velocity of the center of the wheel and its angular velocity; i.e., vc=-r4ωR. Using the unit vectors in the figure above, we can write The velocity of point b is The velocity of point a is The velocity of point d can be written as However, because point d does not slip, we can set From this we can solve for as ωB Author: Kennedy, T. C. Subject: Dynamics Topic: Kinematics of Rigid Bodies Problem Length: 20 minutes Grading: Hand graded Presentation Format: Text and figure with problem statement Other:
Dynamics 109 – Kinematics of Bodies A ring with outer radius r4=2.5in and inner radius r3=2in rolls clockwise without slipping at ωR=10radians/s. The center shaft with radius r1=1in rotates counterclockwise at ωS =5radians/s. Find the angular velocity of the bearings ωB with radius r2=0.5in. There is no slipping at the contact points. Solution: For a wheel that rolls without slipping, there is a simple relation between the velocity of the center of the wheel and its angular velocity; i.e., vc=-r4ωR. Using the unit vectors in the figure above, we can write The velocity of point b is The velocity of point a is The velocity of point d can be written as However, because point d does not slip, we can set From this we can solve for ωB as Author: Kennedy, T. C. Subject: Dynamics Topic: Kinematics of Rigid Bodies Problem Length: 20 minutes Grading: Hand graded Presentation Format: Text and figure with problem statement Other:
Dynamics_Solutions.docx