Rotation about a Fixed Axis - Example Problem 6.6-3

 

In the figure shown, gear A has a mass of 3 kg and is being driven by an engine generating 100 N-m of torque. This gear is then connected via a belt to gear B which has an effective mass of 1 kg and drives an accessory of the engine that has negligible mass and friction. If gear A has a radius of 10 cm and gear B has a radius of 3 cm, determine the angular acceleration of gear B . You may approximate the gears as disks and assume that the belt is inextensible with negligible mass.

 

 

Given:

• m_A = 3 kg
• m_B = 1 kg
• r_A = 0.1 m
• r_B = 0.03 m
• M = 100 N-m

 

Find: α_B

 

Video solution:

 

The following video walks you through the solution to this problem. It is suggested that you try solving the problem first and then, if you have difficulties with the solution, watch the video for help.

 

 

Interactive solution:

 

Draw a separate free-body diagram for gear A and gear B. Click on the figure to see the results.

 

When applying the moment equation to each gear, what point should we use as a reference?

 

The center of the gear to eliminate the support reactions.
Where the belt contacts the gear to eliminate the tension force.