Centripetal Acceleration

A tall baseball player with a forearm length of  $\frac{r}{2}$  throws a ball by rotating their forearm about an axis at their elbow with angular speed $\omega$ . A shorter baseball player with a forearm length of $\frac{r}{4}$ throws a ball by rotating their forearm about an axis at their elbow with the same angular speed $\omega$ . 

How does the linear speed of the tall player's ball $V_{Tall}$   compare with the shorter player's ball $V_{Short}$ ?

•  $V_{tall}=4V_{short}$  
  

•  $V_{tall}=\frac{V_{short}}{2}$  
  

•  $V_{tall}=V_{short}$  
  

•  $V_{tall}=2V_{short}$  
  

A sister spins her brother in a circle of radius R at angular speed  $\omega_i$ . Then the sister decreases her angular speed to  $\frac{1}{2}\omega_i$  with the same radius. 
How does the magnitude of the brother's centripetal acceleration change when the sister slows down?

• No change

• Decreases by a factor of 2

• Increases by a factor of 2

• Decreases by a factor of 4

A black disc spins with angular speed  $2\omega$  and a point on the edge moves at speed  $\upsilon$  . A white disc spins with angular speed  $4\omega$  , with a point on the edge moving at speed  $4\upsilon$ . 

Which disc has a larger radius?

• The white disc has a larger radius.

• Not enough information. 

• They have the same radius.

• The black disc has a larger radius. 

A bicycle racer rides around a circular track of radius R. The racer speeds around its first lap at linear speed $\nu_i$ . Later, their speed decreases to  $\frac{1}{3}\upsilon_i$ . 

How does the magnitude of the racer's centripetal acceleration change after the linear speed decreases?  

• Increases by factor of 3

• Decreases by factor of 3

• Decreases by factor of 9

• No change

An ice skater spins with angular speed $3\omega$ and initial frequency  $f_i$ . She brings her arms away from her body, decreasing her angular speed to  $\omega$ . Her final frequency is  $f_f$ .

How does the frequency of her spin change?  

• They are the same.

• Decreases by a factor of 3.

• Increases by a factor of 3.

• Decreases by a factor of 9.

A wheel with radius  $r$  rotates freely about its axle with initial angular speed of magnitude  $\omega_i$ . A point on the wheel's rim moves at linear speed  $v$ . Suddenly, the wheel accelerates so the point moves at linear speed  $2v$ . The final angular speed is  $\omega_f$ . 

How does the wheel's angular speed change?  

• No change

• Increases by a factor of 4

• Decreases by a factor of 2

• Increases by a factor of 2

A father spins his daughter in a circle of radius $R$  at angular speed  $\omega_i$  . Then the father increases his angular speed to  $3\omega_i$  with the same radius. 

How does the magnitude of the child's centripetal acceleration change when the father speeds up?

• Decreases by factor of 3

• Increases by factor of 3

• Increases by factor of 9

• No change

A large globe spins with angular speed

 $\omega$ . A smaller globe spins with double the angular speed. 

How does the period  $T_{l\arg e}$ of the large globe compare with the period  $T_{small}$  of the small globe?

• Not enough information

•  $T_{l\arg e}=T_{small}$  

•  $T_{l\arg e}=2T_{small}$  

•  $T_{l\arg e}=\frac{1}{2}T_{small}$