Answer to Question #199278 in Mechanical Engineering for Melissa

Question

It is important that the karts can brake effectively. They use drum brakes where a solid circular drum of mass 4.0 kg and radius 0.15 m is rotating at an angular speed of 22 rad s−1 about an axis when a ‘braking’ torque is applied to it which brings it to rest in 5.8 s.

Calculate

i) its angular deceleration when the braking torque is applied.

ii) the moment of inertia of the drum about the axis shown

𝐼 = 1 𝑚𝑟2 2

iii) the resultant torque that causes it to decelerate.

Answer 1

i

$\tau=I \alpha \implies \alpha =\frac{\tau}{I}=\frac{3.55*0.15}{4*0.15^2}=0.169 rad/s^2$

ii

$I=mr^2=4*0.15^2=0.09kgm^2$

iii

$\tau =Fr= 4*(2 \pi*0.15)^2=3.55 Nm$