Wagon
Wheel Structure
Moment of Inertia
Wheel Mass
Wheel Radius

Wagon $A$
Solid disk
$\dfrac{1}{2} M R^2$
$0.5\,\text{kg}$
$0.1\,\text{m}$

Wagon $B$
Solid disk
$\dfrac{1}{2} M R^2$
$0.2\,\text{kg}$
$0.1\,\text{m}$

Wagon $C$
Hollow hoop
$M R^2$
$0.1\,\text{kg}$
$0.1\,\text{m}$

Three wagons have identical total mass (including their wheels) and each has four wheels. However, the wheels on each wagon have different designs with varying mass distributions and radii as shown in a reference chart. When accelerating each wagon from a standstill to $10\,\text{m/s}$, which wagon requires the most energy input?

Question

Wagon
Wheel Structure
Moment of Inertia
Wheel Mass
Wheel Radius

Wagon $A$
Solid disk
$\dfrac{1}{2} M R^2$
$0.5\,\text{kg}$
$0.1\,\text{m}$

Wagon $B$
Solid disk
$\dfrac{1}{2} M R^2$
$0.2\,\text{kg}$
$0.1\,\text{m}$

Wagon $C$
Hollow hoop
$M R^2$
$0.1\,\text{kg}$
$0.1\,\text{m}$

Three wagons have identical total mass (including their wheels) and each has four wheels. However, the wheels on each wagon have different designs with varying mass distributions and radii as shown in a reference chart. When accelerating each wagon from a standstill to $10\,\text{m/s}$, which wagon requires the most energy input?(a) Wagon $A$
, (b) Wagon $B$
, (c) Wagon $C$
, (d) All require the same energy input
:

Rita · Accepted Answer

See how Prof Phy solves this.

Wagon	Wheel Structure	Moment of Inertia	Wheel Mass	Wheel Radius
Wagon \(A\)	Solid disk	\(\dfrac{1}{2} M R^2\)	\(0.5\,\text{kg}\)	\(0.1\,\text{m}\)
Wagon \(B\)	Solid disk	\(\dfrac{1}{2} M R^2\)	\(0.2\,\text{kg}\)	\(0.1\,\text{m}\)
Wagon \(C\)	Hollow hoop	\(M R^2\)	\(0.1\,\text{kg}\)	\(0.1\,\text{m}\)

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