Question

The bike wheel has a mass of 0.825 kg and a radius of 0.385 m. If all the mass of the wheel is assumed to be located on the rim, find the magnitude of the frictional torque that was acting on the spinning wheel.

a) Please provide the magnitude of the frictional torque.
b) Calculate the angular acceleration of the wheel.
c) Determine the rotational kinetic energy of the wheel.
d) Find the linear speed of a point on the wheel's rim.

Answer 1

To find the magnitude of the frictional torque on the spinning wheel, we can use the formulas for torque and moment of inertia. The angular acceleration, rotational kinetic energy, and linear speed can also be calculated using relevant formulas.

Step-by-step explanation:

To find the magnitude of the frictional torque on the spinning wheel, we need to consider the concept of rotational motion. The torque acting on an object can be calculated using the formula:

Torque = Moment of Inertia x Angular Acceleration

In this case, since all the mass of the wheel is located on the rim, we can treat it as a ring and calculate the moment of inertia using the formula:

Moment of Inertia = Mass x (Outer Radius^2 - Inner Radius^2)

After calculating the moment of inertia, we can use the given information about the wheel's mass and radius to find the angular acceleration. The frictional torque can then be calculated using the formula.

b) The angular acceleration of the wheel can be calculated using the formula:

Angular Acceleration = Torque / Moment of Inertia

c) The rotational kinetic energy of the wheel can be calculated using the formula:

Rotational Kinetic Energy = (1/2) x Moment of Inertia x (Angular Velocity)^2

d) The linear speed of a point on the wheel's rim can be calculated using the formula:

Linear Speed = (Angular Velocity) x (Radius)