How much work is done by a 50 N m torque that rotates a wheel through one revolution?

To determine how much work is done by a torque when rotating an object, we can use the formula for work based on torque and the angular displacement in radians. The formula is:

[ \text{Work} = \tau \cdot \theta ]

where ( \tau ) is the torque and ( \theta ) is the angular displacement in radians.

In this case, the torque provided is 50 N m. When the wheel rotates through one complete revolution, the angular displacement is ( 2\pi ) radians (because there are ( 2\pi ) radians in one full revolution).

Now, substituting in the values:

[ \text{Work} = 50 , \text{N m} \cdot 2\pi , \text{radians} ]

Calculating this gives:

[ \text{Work} = 50 \cdot 2 \cdot 3.14 \approx 50 \cdot 6.28 \approx 314 , \text{J} ]

Thus, the work done by the torque of 50 N m in rotating the wheel through one complete revolution is approximately 314 joules. This clearly matches the