A wheel of radius 0.20 m is mounted on a frictionless horizontal axis. The rotational inertia of the wheel about the axis is 0.07 kgm2. A massless cord wrapped around the wheel is attached to a 2.0 kg block that slides on a horizontal frictionless surface. If a horizontal force of magnitude P = 3.0 N is applied to the block as shown in figure, what is the magnitude of the angular acceleration (in r/s2) of the wheel? Assume the string does not slip on the wheel.

Engineering

Physics

Moment of Inertia

Question

A wheel of radius 0.20 m is mounted on a frictionless horizontal axis. The rotational inertia of the wheel about the axis is 0.07 kgm². A massless cord wrapped around the wheel is attached to a 2.0 kg block that slides on a horizontal frictionless surface. If a horizontal force of magnitude P = 3.0 N is applied to the block as shown in figure, what is the magnitude of the angular acceleration (in r/s²) of the wheel? Assume the string does not slip on the wheel.

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P – T = ma       .......... (i)
TR = I_Cα       .......... (ii)
a = αR           .......... (iii)

$P = \frac{I_{C}}{R} α + mαR$

$∴ α = 4 r / s^{2}$

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