Question

A particle travels in circle of radius $20\, cm$ at a speed that uniformly increases. It speed changes from $5 \,m / s$ to $6\, m / s$ in $2 \,s$. The angular acceleration is

• A. $2\, rad \,s ^{-2}$
• B. $2.5 \,rad \,s ^{-2}$
• C. $5 \,rad \,s ^{-2}$
• D. $1.5 \,rad \,s ^{-2}$

Answer 1

Answer: (B)

$a_{t}=\frac{d v}{d t}=\frac{v_{2}-v_{1}}{t_{2}-t_{1}}=\frac{6-5}{2}$
$=0.5 \,m \,s ^{-2}$
$\alpha=\frac{a_{t}}{R}=\frac{0.5}{0.2}$
$=2.5 \,rad \,s ^{-2}$