A circular blade on a radial arm saw is turning at 257 rad/s at the instant the motor is turned off. In 17.0 s the speed of the blade is reduced to 90 rad/s. Assume the blade to be a uniform solid disk of radius 0.170 m and mass 0.400 kg. Find the net torque applied to the blade
We found the change in velocity over time and then multiplied by inertia of a disc. The answer we found was 0.05678. This was incorrect, any suggestions?
acceleration is in fact deltaV/time. The moment of inertia is...http://www.ac.wwu.edu/~vawter/PhysicsNet/Topics/RotationalKinematics/MomentInertia.html
I get The same answer you got, torque is in N-m
Thanks Mr. Pursley. We were correct except the answer was negative.
To find the net torque applied to the blade, we can use the principle of rotational motion that relates torque, moment of inertia, and angular acceleration.
The formula is: Torque = moment of inertia * angular acceleration
First, let's find the moment of inertia for the circular blade. The moment of inertia for a uniform solid disk rotating about its axis is given by the equation:
I = (1/2) * m * r^2
where I is the moment of inertia, m is the mass of the disk, and r is the radius of the disk.
Given the mass of the blade is 0.400 kg and the radius is 0.170 m, we can substitute these values into the equation to find the moment of inertia:
I = (1/2) * 0.400 kg * (0.170 m)^2
I = 0.00688 kg * m^2
Now, let's calculate the angular acceleration using the given information.
Angular acceleration, α = (change in angular velocity) / time
Given the initial angular velocity is 257 rad/s and the final angular velocity is 90 rad/s, and the time to change the velocity is 17.0 s, we can substitute these values into the equation:
α = (90 rad/s - 257 rad/s) / 17.0 s
α = -167 rad/s / 17.0 s
α = -9.82 rad/s^2 (Note: The negative sign indicates that the angular acceleration is in the opposite direction as the initial angular velocity)
Finally, we can calculate the net torque applied to the blade using the formula:
Torque = I * α
Substituting the values we found:
Torque = 0.00688 kg * m^2 * (-9.82 rad/s^2)
Torque = -0.0674 N·m
Therefore, the net torque applied to the blade is approximately -0.0674 N·m.
To find the net torque applied to the blade, we can use the equation:
Net torque = Moment of inertia × Angular acceleration
First, let's calculate the angular acceleration using the given information. We can use the equation:
Angular acceleration = (final angular velocity - initial angular velocity) / time
Angular acceleration = (90 rad/s - 257 rad/s) / 17.0 s
Angular acceleration = -167 rad/s / 17.0 s
Angular acceleration = -9.8235 rad/s²
Next, we need to calculate the moment of inertia of the disk. The moment of inertia for a uniform solid disk is given by the equation:
Moment of inertia = (1/2) × mass × radius²
Moment of inertia = (1/2) × 0.400 kg × (0.170 m)²
Moment of inertia = 0.01156 kg·m²
Now, we can calculate the net torque applied to the blade using the equation stated earlier:
Net torque = Moment of inertia × Angular acceleration
Net torque = 0.01156 kg·m² × (-9.8235 rad/s²)
Net torque = -0.1137 N·m
So, the net torque applied to the blade is approximately -0.1137 N·m. Note that the negative sign indicates that the torque is in the opposite direction of the initial motion of the blade.