Site hosted by Angelfire.com: Build your free website today!
Main Desktop Lessons Desktop Review Desktop Lab Desktop Chart Desktop

    
Nonuniform Circular Motion

Table of Contents

Introduction
Problems

Answers

   

Introduction

When you first start revolving a ball on the end of a string around your head, you must give it tangential acceleration. this is accomplished by pulling on the string with your hand displaced from the center of the circle.

The tangential component of the acceleration, aT, is equal to the rate of change of the magnitude of the velocity of the object.

         /\v                         v2 
aT = -—   while   aC = —--
         /\t                          r

These are perpendicular to each other. a = ( aC2 + aT2 ) 1/2

Since it is a vector you must give the direction.

 

 

 

 

 

 

Table of Contents

    

Problems

1.     Doug is in a racing car starting from rest at the start time. It accelerates to a uniform rate of speed of 43.0 m/s in 12.0 s. He is driving on a circular track with a radius of 600. m. Assuming constant tangential acceleration, calculate (a) tangential acceleration, (b) centripetal acceleration at 40.0 m/s, and (c) Total acceleration at 40.0 m/s.
     
2. Apollo went from rest to 20.0 m/s in 5.00 seconds on the ice skating short track at the 2002 Olympics.  Assuming constant tangential acceleration, calculate (a) tangential acceleration, (b) centripetal acceleration at 4.00 seconds, and (c) Total acceleration at 4.00 seconds.
Table of Contents

      

Answers

1.     Doug is in a racing car starting from rest at the start time. It accelerates to a uniform rate of speed of 43.0 m/s in 12.0 s. He is driving on a circular track with a radius of 600. m. Assuming constant tangential acceleration, calculate (a) tangential acceleration, (b) centripetal acceleration at 40.0 m/s, and (c) Total acceleration at 40.0 m/s.
     
   
       /\v                        v2 
aT = -—   and   aC = —--         and   a = ( aC2 + aT2 ) 1/2
        
/\t                       r
   

        /\v           43.0 m s -1 
aT = -—   =  ----------------- = 3.58 m s -2  

        
/\t            12.0 s
    

            v2         (40.0 m s -1 ) 2 
 aC = —--  =  ---------------------- = 2.67 m s -2  

a = ( aC2 + aT2 ) 1/2  =  ( (3.58 m s -2)2  +  (2.67 m s -2)2 ) 1/2  =  4.47 m s -2  

If the race is run counter-clockwise on the track, the acceleration and force will be to the left of the tangential direction 
   

                           aC                                    2.67 m s -2  
Angle = Tan -1( ------ )  =  Tan -1 ( ------------------ ) = 36.7o  
                           aT                           3.58 m s -2  

 

    

   

2. Apollo went from rest to 20.0 m/s in 5.00 seconds on the ice skating short track at the 2002 Olympics with a radius of 25.0 m.  Assuming constant tangential acceleration, calculate (a) tangential acceleration, (b) centripetal acceleration at 4.00 seconds, and (c) Total acceleration at 4.00 seconds.
     
   
        /\v                        v2 
aT = -—   and   aC = —--         and   a = ( aC2 + aT2 ) 1/2
        
/\t                       r
   

        /\v           20.0 m s -1 
aT = -—   =  ----------------- = 4.00 m s -2  

        
/\t            5.00 s
    

v = at = 4.00 m s -2 x 4.00 s  =  16.0 m s -1  
  

            v2         (20.0 m s -1 ) 2 
 aC = —--  =  ---------------------- = 16.0 m s -2  

r              25.0 m    
   

a = ( aC2 + aT2 ) 1/2  =  ( (4.00 m s -2)2  +  (16.0 m s -2)2 ) 1/2  =  16.5 m s -2  

If the race is run counter-clockwise on the track, the acceleration and force will be to the left of the tangential direction 
   

                           aC                                    16.0 m s -2  
Angle = Tan -1( ------ )  =  Tan -1 ( ------------------ ) = 76.0o  
                           aT                           4.00 m s -2  

 

 

Table of Contents