Question

An old grindstone, used for sharpening tools, is a solid cylindrical wheel that can rotate about its central axle with negligible friction. The radius of the wheel is 0.330 m. A constant tangential force of 200 N applied to its edge causes the wheel to have an angular acceleration of 0.844 rad/s2.

What is the moment of inertia of the wheel (in kg · m2)?
________kg · m2

What is the mass (in kg) of the wheel?
_______kg

The wheel starts from rest and the tangential force remains constant over a time period of 4.00 s. What is the angular speed (in rad/s) of the wheel at the end of this time period?
_______rad/s

Answer 1

(a) The moment of inertia of the wheel  is 78.2 kgm².

(b) The mass (in kg) of the wheel is 1,436.2 kg.

(c) The angular speed (in rad/s) of the wheel at the end of this time period is 3.376 rad/s.

Moment of inertia of the wheel

Apply principle of conservation of angular momentum;

Fr = Iα

where;

• F is applied force
• r is radius of the cylinder
• α is angular acceleration
• I is moment of inertia

I = Fr/α

I = (200 x 0.33) / (0.844)

I = 78.2 kgm²

Mass of the wheel

I = ¹/₂MR²

where;

• M is mass of the solid cylinder
• R is radius of the solid cylinder
• I is moment of inertia of the solid cylinder

2I = MR²

M = 2I/R²

M = (2 x 78.2) / (0.33²)

M = 1,436.2 kg

Angular speed of the wheel after 4 seconds

ω = αt

ω = 0.844 x 4

ω = 3.376 rad/s

Thus, the moment of inertia of the wheel  is 78.2 kgm².

The mass (in kg) of the wheel is 1,436.2 kg.

The angular speed (in rad/s) of the wheel at the end of this time period is 3.376 rad/s.

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