You have just bought a new bicycle. On your first riding trip, it seems that the bike comes to rest relatively quickly after you stop pedaling and let the bicycle coast on flat ground. You call the bicycle shop from which you purchased the vehicle and describe the problem. The technician says that they will replace the bearings in the wheels or do whatever else is necessary if you can prove that the frictional torque in the axle of the wheels is worse than -0.02 N. m. At first, you are discouraged by the technical sound of what you have been told and by the absence of any tool to measure torque in your garage. But then you remember that you are taking a physics class! You take your bike into the garage, turn it upside down and start spinning the wheel while you think about how to determine the frictional torque. The driveway outside the garage had a small puddle, so you notice that droplets of water are flying off the edge of one point on the tire tangentially, including drops that are projected straight upward, as shown in the figure below. --ov = 0 Ah-ha! Here is your torque-measuring method! The upward-projected drops leave the rim of the wheel at the same level as the axle. You measure the height to which a drop rises from the level of the axle: h₁ = 47.0 cm. The wet spot on the tire makes one revolution and another drop is projected upward. You measure its highest point: h₂42.0 cm. You measure the radius of the wheel: r= 0.311 m. Finally, you take the wheel off the bike and find its mass: m=0.900 kg. Because most of the mass of the wheel is at the tire, you model the wheel as a hoop. What do you tell the technician when you call back? (Enter the frictional torque, in N. m, that you tell to the technician. Assume the positive direction is clockwise. Indicate the direction with the sign of your answer.) N.m

While working as an intern in a blacksmith's shop, you realize that the brake on the sharpening stone (a stone uniform disk) is no longer working. To stop the rotation at the end of the day, you put your knowledge of physics to good use and use a steel axe to stop the rotation. You press the steel axe against the stone using a radial force of 19.5 N. The stone is originally rotating at a rate of 85 revolutions per minute (out of the page), has a radius of 0.350 m, and a mass of 91.0 kg. Choose out of the page to be positive. a) Given a coefficient of kinetic friction between the stone and the axe equal to 0.20, what is the angular acceleration of the sharpening stone? b) What angular displacement did the stone turn through from its initial angular speed to when the stone stops rotating?

Each propeller on a King Air twin-engine airplane consists of three blades, each of mass 21 kg and length 121 cm. The blades may be treated approximately as uniform, thin rods. What is the rotational inertia of the propeller, and if the propeller is driven by an engine that develops a torque of 2650 N⋅m, how long will it take to change the propeller's angular speed from 1250 rpm to 1850 rpm?

A uniform ladder 5.0 m long rests against a frictionless, vertical wall with its lower end 3.0 m from the wall. The ladder weighs 140 N. A man weighing 620 N climbs slowly up the ladder. Start by drawing a free-body diagram of the ladder. What is the actual frictional force when the man has climbed 1.0 m along the ladder? [Hint: Draw a free body diagram to determine what forces are at play. Then use the torque formula (T = Fxrx sine) to find the net torque.]