Rotational Kinematics Practice

Sample questions

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1. Sample 1difficulty 1/5

   Starting from rest, a disk undergoes an angular acceleration of $2.0~\text{rad/s}^2$ for $5.0~\text{s}$. What is its final angular velocity?

   • A

     $0.4~\text{rad/s}$

   • B

     $10~\text{rad/s}$

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   • C

     $7.0~\text{rad/s}$

   • D

     $2.5~\text{rad/s}$

   Why

   $\omega = \omega_0 + \alpha t = 0 + (2.0)(5.0) = 10~\text{rad/s}$.

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2. Sample 2difficulty 2/5

   A wheel's angular velocity rises linearly from $0$ to $20~\text{rad/s}$ over $4~\text{s}$, then remains constant. Through what total angle does it rotate during the first $8~\text{s}$?

   • A

     $40~\text{rad}$

   • B

     $120~\text{rad}$

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   • C

     $160~\text{rad}$

   • D

     $80~\text{rad}$

   Why

   Angle = area under $\omega$-vs-$t$ = $\tfrac{1}{2}(4)(20) + (4)(20) = 40 + 80 = 120~\text{rad}$.

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3. Sample 3difficulty 2/5

   A wheel slows uniformly from $20~\text{rad/s}$ to rest in $4~\text{s}$. Its angular acceleration is

   • A

     $+5~\text{rad/s}^2$

   • B

     $-20~\text{rad/s}^2$

   • C

     $-5~\text{rad/s}^2$

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   • D

     $+80~\text{rad/s}^2$

   Why

   $\alpha = (0 - 20)/4 = -5~\text{rad/s}^2$.

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4. Sample 4difficulty 2/5

   A turntable spins up from rest with constant angular acceleration $\alpha = 3.0~\text{rad/s}^2$ for $4.0~\text{s}$. Through what angle has it rotated?

   • A

     $24~\text{rad}$

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   • B

     $48~\text{rad}$

   • C

     $6~\text{rad}$

   • D

     $12~\text{rad}$

   Why

   $\theta = \tfrac{1}{2}\alpha t^2 = \tfrac{1}{2}(3.0)(4.0)^2 = 24~\text{rad}$.

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5. Sample 5difficulty 2/5

   A wheel starting from rest has angular acceleration $5~\text{rad/s}^2$. Through what total angle has it rotated after $4.0~\text{s}$?

   • A

     $80~\text{rad}$

   • B

     $10~\text{rad}$

   • C

     $40~\text{rad}$

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   • D

     $20~\text{rad}$

   Why

   $\theta = \tfrac{1}{2}\alpha t^2 = \tfrac{1}{2}(5)(16) = 40~\text{rad}$.

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