A 85.6 g drink is left on a turntable causing it to turn with an angular speed of 8.20 rad/s. If the drink has coefficients of friction of μs = 0.830 and μk = 0.520 with the turntable, what is the furthest distance that the drink could have been placed from the centre of the turntable for the drink not to slide?

The dung beetle is known as one of the strongest animals for its size, often forming balls of dung up to 10 times their own mass and rolling them to locations where they can be buried and stored as food. A typical dung ball formed by the species K. nigroaeneus has a radius of 1.80 cm and is rolled by the beetle at 6.15 cm/s. HINT (a) What is the rolling ball's angular speed (in rad/s)? rad/s (b) How many full revolutions are required if the beetle rolls the ball a distance of 2.40 m? rev

A small 700 g ball on the end of a thin, light rod is rotated in a horizontal circle of radius 2.5 m.  Calculate the torque needed to keep the ball rotating at a constant angular speed if the air resistance experienced by the ball is 0.0200 N.   Ignore the rods moment of inertia and air resistance.  Hint:  Treat the small ball as a particle.

In the figure here, a cylinder having a mass of 2.8 kg can rotate about its central axis through point O. Forces are applied as shown: F1= 9.7 N, F2 = 8.3 N, F3 = 1.8 N, and F4 = 4.5 N. Also, r = 4.3 cm and R = 10 cm. Taking the clockwise direction to be negative, find the angular acceleration of the cylinder. (During the rotation, the forces maintain their same angles relative to the cylinder.) %3D Rotation axis Number Unit

A rock tied to the end of string swings at a constant angular rate. If you are told that the string can support a total of 85 N of force before breaking, what is the maximum angular velocity the rock can rotate if the rock has a mass of 0.16 kg, and the length of the string is 0.5 m? Give your answer in units of radian per second

In the figure here, a cylinder having a mass of 2.7 kg can rotate about its central axis through point O. Forces are applied as shown: F₁ = 8.0 N, F₂ = 9.6 N, F3 = 6.0 N, and F4 = 6.4 N. Also, r = 5.4 cm and R = 10 cm. Taking the clockwise direction to be negative, find the angular acceleration of the cylinder. (During the rotation, the forces maintain their same angles relative to the cylinder.) Number IN Unit Rotation axis F₁ R 0

A car is undergoing an emissions test. The car is stationary on rollers while the gas pedal is depressed until the speedometer reads 60 km/h. The wheels are 54 cm in diameter. Find their angular speed.

An automobile engine can produce 253 Nm of torque. Calculate the angular acceleration (in rad/s2) produced if 80.2% of this torque is applied to the drive shaft, axle, and rear wheels of a car, given the following information. The car is suspended so that the wheels can turn freely. Each wheel acts like a 15.0 kg disk that has a 0.180 m radius. The walls of each tire act like a 2.00 kg annular ring that has inside radius of 0.180 m and outside radius of 0.320 m. The tread of each tire acts like a 10.0 kg hoop of radius 0.330 m. The 12.1 kg axle acts like a rod that has a 2.00 cm radius. The 29.7 kg drive shaft acts like a rod that has a 3.20 cm radius. rad/s² t Additional Materials Reading

A 8.6-cm-diameter, 389 g sphere is released from rest at the top of a 3.2-m-long, 25° incline. It rolls, without slipping, to the bottom. (a) What is the sphere's angular velocity at the bottom of the incline?

Mary and her younger brother Alex decide to ride the carousel at the State Fair. Mary sits on one of the horses in the outer section at a distance of 2.0 m from the center. Alex decides to play it safe and chooses to sit in the inner section at a distance of 1.3 m from the center. The carousel takes 5.6 s to make each complete revolution. (a) What is Mary's angular speed ?M and tangential speed vM? (b) What is Alex's angular speed ?A and tangential speed vA?