Two flywheels of negligible mass and different radii are bonded together and rotate about a common axis (see below). The smaller flywheel of radius 21 cm has a cord that has a pulling force of 50 N on it. What pulling force (in N) needs to be applied to the cord connecting the larger flywheel of radius 34 cm such that the combination does not rotate? E = ? 50 N

A pulley with moment of inertia I = 0.75 kg-m² and radius R = 15 cm is mounted on a wall. A light string is wrapped around the pulley with a mass m = 2.0 kg attached to the end. The pulley rotates as the mass falls. Use Newton's second law to calculate the acceleration of the mass. Check that your formula gives the expected behavior when I →0. => To help get started, the free body diagrams m and the pulley is shown below. T m Write down Newton's second law for each diagram. Use (and explain) the relationship R a = RO TIL R T

The figure below represents a bicycle wheel comprised of a rim with a radius of R = 0.5 m and mass of M = 200 g, to which someone has added two m = 30 g sensors that are separated by an angle of = 110°. The axis of rotation for the wheel is at its center, as represented by the vector symbol, for a direction into the page. m = 30 g R = 0.5 m M = 200 g m = 30 g a) Where is the center of mass of the wheel/sensor system? b) What is the rotational moment of inertia of the wheel/sensor system around its axis of rotation?

Two blocks are connected by massless string that is wrapped around a pulley. Block 1 has a mass m1=6.00 kg, block 2 has a mass m2=2.00 kg, while the pulley has a mass of 1.00 kg and a radius of 18.0 cm. When the pulley turns, there is friction in the axel that exerts a torque of magnitude 0.410 N m. If block 1 is released from rest at a height h=1.40 m, how long does it take to drop to the floor?

A bicyclist notes that the pedal sprocket has a radius of rp = 9.5 cm while the wheel sprocket has a radius of rw = 4.5 cm. The two sprockets are connected by a chain which rotates without slipping. The bicycle wheel has a radius R = 62 cm. When pedaling the cyclist notes that the pedal rotates at one revolution every t = 1.2 s. When pedaling, the wheel sprocket and the wheel move at the same angular speed. a)Calculate the angular speed of the pedal sprocket ωp and wheel sprocket ωw in radians per second.  b)Calculate the linear speed of the outer edge of the pedal sprocket vp, in centimeters per second.  c)Calculate the linear speed of the bicycle v, in meters per second, assuming the wheel does not slip across the ground.

An Atwood's machine consists of blocks of masses m₁ = 13.0 kg and m₂ = 19.0 kg attached by a cord running over a pulley as in the figure below. The pulley is a solid cylinder with mass M = 6.80 kg and radius r = 0.200 m. The block of mass m₂ is allowed to drop, and the cord turns the pulley without slipping. M T₁ T₂ Q (a) Why must the tension T₂ be greater than the tension T₁? This answer has not been graded yet. (b) What is the acceleration of the system, assuming the pulley axis is frictionless? (Give the magnitude of a.) m/s² (c) Find the tensions T₁ and T₂- T₁ = T₂ =

An Atwood's machine consists of blocks of masses m₁ = 13.0 kg and m₂ = 24.0 kg attached by a cord running over a pulley as in the figure below. The pulley is a solid cylinder with mass M = 7.60 kg and radius r = 0.200 m. The block of mass m., is allowed to drop, and the cord turns the pulley without slipping. M T2 Q (a) Why must the tension 7₂ be greater than the tension 7₁? This answer has not been graded yet. (b) What is the acceleration of the system, assuming the pulley axis is frictionless? (Give the magnitude of a.) m/s² (c) Find the tensions T, and T₂. T₁ = T2₂ =

A bicyclist notes that the pedal sprocket has a radius of rp = 8.5 cm while the wheel sprocket has a radius of rw = 6.5 cm. The two sprockets are connected by a chain which rotates without slipping. The bicycle wheel has a radius R = 64 cm. When pedaling the cyclist notes that the pedal rotates at one revolution every t = 1.8 s. When pedaling, the wheel sprocket and the wheel move at the same angular speed. a.  Calculate the angular speed of the pedal sprocket ωp, in radians per second.  b. Calculate the linear speed of the outer edge of the pedal sprocket vp, in centimeters per second.  c.  Calculate the angular speed of the wheel sprocket ωw, in radians per second.  d.  Calculate the linear speed of the bicycle v, in meters per second, assuming the wheel does not slip across the ground.

Two flywheels of negligible mass and different radii are bonded together and rotate about a common axis (see below). The smaller flywheel of radius 20 cm has a cord that has a pulling force of 50 N on it. What pulling force (in N) needs to be applied to the cord connecting the larger flywheel of radius 34 cm such that the combination does not rotate? 50 N N

Two buckets of mass ?1=17.5 kg and ?2=15.1 kg are attached to the ends of a massless rope which passes over a pulley with a mass of ?p=8.53 kg and a radius of ?p=0.450 m. Assume that the rope does not slip on the pulley, and that the pulley rotates without friction. The buckets are released from rest and begin to move. If the larger bucket is a distance ?0=2.05 m above the ground when it is released, with what speed ? will it hit the ground?