Physics: Angular Acceleration of Rotational Objects

label Physics
account_circle Unassigned
schedule 1 Day
account_balance_wallet $5

A bicycle wheel has a diameter of 63.8 cm and a mass of 1.79 kg. Assume that the wheel is a hoop with all of the mass concentrated on the outside radius. The bicycle is placed on a stationary stand and a resistive force of 117 N is applied tangent to the rim of the tire.

(a) What force must be applied by a chain passing over a 8.92-cm-diameter sprocket in order to give the wheel an acceleration of 4.49 rad/s2? (b) What force is required if you shift to a 5.65-cm-diameter sprocket? 

Oct 21st, 2017

Thank you for the opportunity to help you with your question!

Torque = Inertia x alpha (angular acceleration rad/s^2) 
Torque also equals force x radius 

First of all lets find the inertia of the wheel. 

hoop = mr^2 = 1.79 x 0.319^2 = 0.18215kg-m^2 

Now, Torque = 0.18215 x 4.49= 0.8178/radius= force

0.8178 x 0.0446 =36.47N

What force must be applied to attain acc of 4.49 rad/s^2? 

17.33 N 

117 N x 0.316 m = 36.972 Nm 

36.972/ 0.0446 = 828.96 N 

Total = 17.33 + 828.96= 846.29 N (answer) 

What force is required if the chain shifts to a 5.65 cm diameter sprocket? 

the torque is the same and divide by the radius

The answer comes out to be 1390.9 N

Please let me know if you need any clarification. I'm always happy to answer your questions.
Jul 6th, 2015

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
Oct 21st, 2017
Oct 21st, 2017
Oct 22nd, 2017
Mark as Final Answer
Unmark as Final Answer
Final Answer

Secure Information

Content will be erased after question is completed.

Final Answer