Examples
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Questions with Suggestions |
1. Same bike odometer, different diameter tires. Problem?
Are the circumferences the same?
2. Does a disk rotating with constant angular velocity have tangential and/or radial acceleration?
What happens if there is a tangential acceleration in addition to a radial one. Can the linear velocity be constant? If the linear velocity is constant what does this say about the original statement (constant angular velocity)?
3. Is it possible for a non-rigid body to have a single value of the angular velocity?
Remember the discussion about angular velocity of points on a rigid body versus tangential velocity of points on a rigid body. How can this be true for a non-rigid body?
4. Can a small force ever exert a greater torque than a larger force?
Torque is defined as Force times length of the lever arm. The force is at 90 degrees to the lever arm. What happens if the length of the arm increases?
8. Running animals with most of mass of leg near body - why?
Look at moment of inertial when mass is concentrated near body. Less torque is required for a given angular acceleration.
1. Converting between radians and degrees.
Use the following ratio and solve for the quantity needed, radians in this case Degrees/360 = Radians/2 p
Radians = p x Degrees/180
4. Blades rotate at given rpm (revolutions per minute). Turn off the motor and the blades stop in given amount of time. What is angular
acceleration as blades slow down?
We can use dimensional analysis to solve for the initial angular acceleration in radians per second. Remember dimensional analysis from chapter 1 and some of you asking why bother studying such a thing?
(revolutions/min)x (2p radians/revolution)(1 minute/60 seconds) = radians per second
Once we have the angular velocity we can find the acceleration from the definition which is the change in the angular velocity (the quantity above - 0) divided by time which is given.