Question

A playground ride consists of a disk of mass M = 49 kg and radius R = 1.7 m mounted on a low-friction axle. A child of mass m = 29 kg runs at speed v = 2.6 m/s on a line tangential to the disk and jumps onto the outer edge of the disk.

Answer 1

Answer:

The angular speed is 0.83 rad/s.

Explanation:

Given that,

Mass of disk M=49 kg

Radius = 1.7 m

Mass of child m= 29 kg

Speed = 2.6 m/s

Suppose if the disk was initially at rest , now how fast is it rotating

We need to calculate the angular speed

Using conservation of momentum

$m\omega_{i}=(mr^2+\dfrac{Mr^2}{2})\omega_{f}$

$mvR=(mr^2+\dfrac{Mr^2}{2})\omega$

Put the value into the formula

$29\times2.6\times1.7=(29\times1.7^2+\dfrac{49\times1.7^2}{2})\omega_{f}$

$\omega_{f}=\dfrac{29\times2.6\times1.7}{(29\times1.7^2+\dfrac{49\times1.7^2}{2})}$

$\omega_{f}=0.83\ rad/s$

Hence, The angular speed is 0.83 rad/s.