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what is the formula for the torque on the turntable in terms of tension t in the string and the lever arm distance r?

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Final answer:

Torque on a turntable can be calculated using the formula T = rF sin θ, where T stands for torque, r is the lever arm distance, F is the force, and θ is the angle between the force and the lever arm. When tension acts perpendicularly, the formula simplifies to T = rt.

Step-by-step explanation:

The formula for torque on a turntable in terms of the tension t in the string and the lever arm distance r can be expressed as T = rF sin θ, where T is the torque, r is the lever arm distance, F is the magnitude of the force, which in this case is the tension t in the string, and θ is the angle between the tension force and the lever arm.

For a string pulling tangentially on a turntable, this angle is 90 degrees, making the sin of this angle equal to 1, which simplifies the torque expression to T = rt when the tension is applied perpendicularly to the turntable arm.

It's important to note that the SI unit for torque is the newton-meter (N-m) and by convention, counterclockwise torques are considered positive.

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