Question

A grinding wheel is in the form of a uniform solid disk of radius 7.10 cm and mass 2.07 kg. It starts from rest and accelerates uniformly under the action of the constant torque of 0.599 N �� m that the motor exerts on the wheel. What is the angular acceleration of the grinding wheel?

Answer 1

To find the angular acceleration of the grinding wheel, you can use Newton's second law for rotation, τ = Iα, along with the formula for the moment of inertia of a solid disk. After calculating I, insert the given torque to solve for the angular acceleration α.

Step-by-step explanation:

To calculate the angular acceleration of the grinding wheel, we need to apply Newton's second law for rotation, which relates torque (τ), moment of inertia (I), and angular acceleration (α) as follows: τ = Iα. The moment of inertia for a solid disk is I = ½MR², where M is the mass of the disk, and R is its radius. Plugging in the provided values for the mass (2.07 kg) and radius (7.10 cm or 0.071 m), we get I = ½(2.07 kg)(0.071 m)².

Using the given torque of 0.599 N·m, we can solve for the angular acceleration with the equation: 0.599 N·m = Iα. After calculating the moment of inertia, we substitute it into the equation to find α, giving us the angular acceleration of the grinding wheel.