Question

What is the angular momentum of a 2.7-kg uniform cylindrical grinding wheel of radius 29 cm when rotating at 1400 rpm? How much torque is required to stop it in 7.0 s?

Torque:
The torque is referred to as the torsional effect of the system. The torque can create angular displacement in the system. The magnitude of torque can be determined by the fraction of change in angular momentum with time interval.

Answer 1

The angular momentum of the grinding wheel can be calculated using the formula Angular Momentum = moment of inertia x angular velocity. The torque required to stop the wheel can be found using the formula Torque = change in angular momentum / time.

Step-by-step explanation:

To find the angular momentum of the grinding wheel, we need to use the formula:

Angular Momentum = moment of inertia x angular velocity

The moment of inertia of a uniform cylindrical object is given by I = 0.5 x mass x radius^2. Therefore, the moment of inertia of the grinding wheel can be calculated as: I = 0.5 x 2.7 kg x (0.29 m)^2.

The angular velocity needs to be converted from rpm to rad/s. This can be done by multiplying the rpm by 2π/60, since there are 2π radians in a full revolution and 60 seconds in a minute. So, the angular velocity is: ω = 1400 rpm x 2π/60.

Once we have the moment of inertia and angular velocity, we can substitute these values into the formula to find the angular momentum of the grinding wheel.

To determine the torque required to stop the wheel, we can use the formula: Torque = change in angular momentum / time. The change in angular momentum can be calculated by subtracting the final angular momentum (which is 0, since the wheel is stopping) from the initial angular momentum.

Substituting the values into the formula will give us the torque required to stop the wheel.