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A grinding wheel is designed to spin at 3600 revolutions per minute (RPM) while working against a friction force of 10 newtons applied at the rim of the wheel. The grinding wheel has a radius of .10 m.

a. What is the torque due to friction on the wheel?
b. What is the angular velocity of the wheel?
c. What power must the motor supply to meet this specification?

1 Answer

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Answer:

a. Torque due to friction on the wheel

Torque is the force applied to an object multiplied by the distance from the pivot point to the point where the force is applied. In this case, the force is 10 newtons and the distance is 0.10 meters, so the torque is:

τ = Fr = (10 N)(0.10 m) = 1 Nm

Therefore, the torque due to friction on the wheel is 1 Nm.

b. Angular velocity of the wheel

Angular velocity is the rate of change of an object's angular position. It is measured in radians per second (rad/s). In this case, the wheel is spinning at 3600 revolutions per minute (RPM). To convert to rad/s, we use the following conversion factor:

1 RPM = 2π rad/60 s

Therefore, the angular velocity of the wheel is:

ω = (3600 RPM)(2π rad/60 s) = 360π rad/s

Therefore, the angular velocity of the wheel is 360π rad/s.

c. Power required by the motor

Power is the rate at which work is done. It is measured in watts (W). In this case, the motor must supply enough power to overcome the friction force and maintain the wheel's angular velocity. The power required by the motor is:

P = τω = (1 Nm)(360π rad/s) = 3600π W

Therefore, the power required by the motor is 3600π W.

Step-by-step explanation:

yes

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