A toy car is rolling down the ramp as shown in the figure. The car's mass is m 1.2 kg and the ramp makes an angle of 8-16 degrees with respect to the horizontal. Assume the car is y₁ rolling without friction.

A gyroscope is a top-like toy consisting of a heavy ring attached by light spokes to a central axle. The axle and ring are free to turn on bearings. To get the gyroscope spinning, a 30-cm-long string is wrapped around the 2.0-mm-diameter axle, then pulled with a constant force of 5.0 N. If the ring’s diameter is 5.0 cm and its mass is 30 g, at what rate is it spinning, in rpm, once the string is completely unwound?

When opening a door, you push on it perpendicularly with a force of 55 N at a distance of 0.75 m from the hinges. What torque, in newton meters, are you exerting relative to the hinges?

We hang a body on a 2.0 m long string and lift it so that the string forms an angle of 40° with the vertical axis, and lower. At what angular velocity does the system move at the moment it goes through an equilibrium position?

You have a grindstone (a disk) that is 93.0 kg, has a 0.370-m radius, and is turning at 63.0 rpm, and you press a steel axe against it with a radial force of 14.0 N. (a) Assuming the kinetic coefficient of friction between steel and stone 0.40, calculate the angular acceleration (in rad/s?) of the grindstone. (Indicate the direction with the sign of your answer.) rad/s2 (b) How many turns (in rev) will the stone make before coming to rest? rev

While driving an automobile, the driver makes a left turn. To perform this maneuver, the driver exerts a torque with a magnitude of 3.5 N•m on the rim of the steering wheel. If the radius of the wheel is 0.15 m, what is the magnitude of the force applied by the driver?

When you lift an object by moving only your forearm, the main lifting muscle in your arm is the biceps. Suppose the mass of a forearm with hand is 1.80 kg. If the biceps is connected to the forearm a distance of 2.50 cm from the elbow, what is the magnitude of the torque exerted by the biceps to hold a 44.5 N (about 10 lbs) ball at the end of the forearm at distance of 35.0 cm from the elbow, with the forearm parallel to the floor, in N·m? Use g = 10.0 m/s2.

A block (mass = 3.0kg) is hanging from a mass-less string that is wrapped around a pulley. The string is 120cm long. Initially the string was wrapped fully and the pulley is prevented from rotating and the block is stationary. Then, the pulley is allowed to rotate as the block falls. Assume that the radius of the cord around the pulley remains constant at a value of 0.050m during the block's descent. The mass rolls from rest down to the end of the string. Find the transnational kinetic energy. Find the rotational kinetic energy. Find the angular speed.

Two buckets of mass ?1=21.1 kg and ?2=11.9 kg are attached to the ends of a massless rope which passes over a pulley with a mass of ?p=8.13 kg and a radius of ?p=0.350 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=1.85 m above the ground when it is released, with what speed ? will it hit the ground?

A box of unknown mass is suspended from the end of a strong, thin wire. The other end of the wire is wrapped around the outer rim of a solid disk whose massis 11.0 kg and radius is 54.0 cm. The disk turns on a frictionless axle through its center. The box travels a distance 12.0 m during a time interval of 3.40 s starting from rest.Find the mass of the box.