A large grinding wheel in the shape of a solid cylinder of radius 0.330 m is free to rotate on a frictionless, vertical axle. A constant tangential force of 210 N applied to its edge causes the wheel to have an angular acceleration of 1.161 rad/s2.

(b) What is the mass of the wheel?

torque= momentInertia*angacceleration

210*.330= moment Inertia*1.161

look up the momentu of inertia here:http://www.physics.uoguelph.ca/tutorials/torque/Q.torque.inertia.html
and solve for mass

pito

To find the mass of the wheel, we need to understand the relationship between force, mass, and acceleration.

The torque (τ) exerted on an object is given by the equation τ = Iα, where I is the moment of inertia and α is the angular acceleration.

For a solid cylinder rotating around its axis, the moment of inertia is given by I = 0.5 * m * r^2, where m is the mass of the cylinder and r is its radius.

The torque exerted on the wheel can be calculated using the equation τ = r * F, where r is the radius and F is the force applied tangentially to the edge.

Equating the two torque equations, we have:

r * F = I * α

Substituting the formulas for I and τ, we get:

r * F = (0.5 * m * r^2) * α

Simplifying the equation:

r * F = 0.5 * m * r^2 * α

Dividing both sides by r:

F = 0.5 * m * r * α

Now we can rearrange the equation to solve for the mass (m):

m = (2 * F) / (r * α)

Plugging in the given values:

F = 210 N (the constant tangential force applied to the wheel)
r = 0.330 m (the radius of the wheel)
α = 1.161 rad/s^2 (the angular acceleration of the wheel)

m = (2 * 210 N) / (0.330 m * 1.161 rad/s^2)

Calculating the final result:

m ≈ 1080 kg

Therefore, the mass of the wheel is approximately 1080 kg.