Tutorial 13 Planar dynamics of rigid body Zhengjian, XU DEC 3rd, 2008

Rotation about a fixed axis for a mass point Angular momentum:

Where H is the angular momentum with respect to the center of mass

Calculation of moment of inertia Circle: Rectangle: A bar: A BO L x y O O x y b h R

Another method: parallel-axis method

Example 1 A horizontal force F = 30 lb is applied to the 230-lb refrigerator as shown. Friction is negligible. (a) What is the magnitude of the refrigerator’s acceleration? (b) What normal forces are exerted on the refrigerator by the floor at A and B?

Solution: Assume the box doesnot tip over, then the box has only horizontal velocity and acceleration. NANA NBNB F G 28in 60in 28in V x, a x Force equilibrium: What’s the condition of F for tipping? O

Example 2 Bar AB rotates with a constant angular velocity of 10 rad/s in the counterclockwise direction. The masses of the slender bars BC and CDE are 2 kg and 3.6 kg, respectively. The y axis points upward. Determine the components of the forces exerted on bar BC by the pins at B and C at the instant shown.

BxBx ByBy CyCy CxCx B C C D ECxCx CyCy 1. Dynamics analysis: G Moment equlibrium equations

BxBx ByBy CyCy CxCx 2 Kinematics analysis B C C D E VBVB VCVC At this instant, point A is the instantaneous center of BC. CxCx CyCy From AB-BC: From CD:

From the kinematics analysis: