First slide

Kinematics of rotational motion about fixed axis

Question

A 150 kg merry go round in the shape of a uniform solid horizontal disk of radius 2 m is set in motion by wrapping a rope about the rim of the disk and pulling on the rope. What constant force must be exerted on the rope to bring the merry go round from rest to an angular speed of 0.5 rev/s in 2 sec?

Easy

A

157 N
B

574 N
C

314 N
D

81 N

Solution

$\begin{array}{l} τ = I α \Rightarrow F . r = I \frac{ω_{2} - ω_{1}}{Δ t} \\ \Rightarrow F \times 2 = \frac{1}{2} m r^{2} . \frac{0.5 \times 2 π - 0}{2} \\ \Rightarrow F = 314 N \end{array}$

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