Question

A 6 N force is applied to a cord wrapped around a Pulley of mass 5 kg and radius 20 cm. What is the angular acceleration of the Pulley ?​

Answer 1

AnswEr :

• Linear Force (F) = 6 N
• Mass (m) = 5 kg
• Radius (r) = 20cm = 0.2 m

Firstly, we'll calculate value of linear acceleration. Then by using relationship between radius, linear acceleration and angular acceleration we can find, magnitude of Angular acceleration.

$\longrightarrow \tt{F\ =\ ma} \\ \\ \\ \longrightarrow \tt{a\ =\ \dfrac{F}{m}} \\ \\ \\ \longrightarrow \underline{\boxed{\frak{a\ =\ \dfrac{6}{5}\ ms^{-2}}}}$

Now, use formula for relationships between linear acceleration and angular acceleration.

$\longrightarrow \tt{a\ =\ \alpha r } \\ \\ \\ \longrightarrow \tt{\alpha\ =\ \dfrac{a}{r}} \\ \\ \\ \longrightarrow \tt{\alpha\ =\ \dfrac{6}{\dfrac{5}{0.2}}} \\ \\ \\ \longrightarrow \tt{\alpha\ =\ \dfrac{1.2}{0.5}} \\ \\ \\ \longrightarrow \underline{\boxed{\frak{\alpha\ =\ 2.4\ rads^{-2}}}}$