Molecular Physics | Thermodynamics Answers

It has been suggested that rotating cylinders about 14.0 mi long and 3.94 mi in diameter be placed in space and used as colonies. What angular speed must such a cylinder have so that the centripetal acceleration at its surface equals the free-fall acceleration on Earth?

___rad/s

A 44.0-cm diameter disk rotates with a constant angular acceleration of 2.60 rad/s². It starts from rest at t = 0, and a line drawn from the center of the disk to a point P on the rim of the disk makes an angle of 57.3° with the positive x-axis at this time.

(a) At t = 2.47 s, find the angular speed of the wheel.

 __rad/s

(b) At t = 2.47 s, find the magnitude of the linear velocity and tangential acceleration of P.

linear velocity ___ m/s

tangential acceleration ___ m/s²

(c) At t = 2.47 s, find the position of P (in degrees, with respect to the positive x-axis).

___ ° counterclockwise from the +x-axis

A bicyclist starting at rest produces a constant angular acceleration of 1.50 rad/s² for wheels that are 33.5 cm in radius.

(a) What is the bicycle's linear acceleration (in m/s²)? (Enter the magnitude.)

___ m/s²

(b) What is the angular speed of the wheels (in rad/s) when the bicyclist reaches 10.2 m/s?

___rad/s

(c) How many radians have the wheels turned through in that time?

___rad

(d) How far (in m) has the bicycle traveled?

___m

A bicycle tire is spinning counterclockwise at 2.60 rad/s. During a time period Δt = 1.75 s, the tire is stopped and spun in the opposite (clockwise) direction, also at 2.60 rad/s. Calculate the change in the tire's angular velocity Δ𝜔 and the tire's average angular acceleration 𝛼_av. (Indicate the direction with the signs of your answers.)

(a) the change in the tire's angular velocity Δ𝜔 (in rad/s)

 ___rad/s

(b) the tire's average angular acceleration 𝛼_av (in rad/s²)

___rad/s²

A car of mass m follows a truck of mass 2m around a circular turn. Both vehicles move at speed v.

(a) What is the ratio of the truck's net centripetal force to the car's net centripetal force?

F_truck

____

F_car = 

(b) At what new speed v_truck will the net centripetal force acting on the truck equal the net centripetal force acting on the car still moving at the original speed v? State your answer in terms of v.

v_truck =  

A disk rotates about an axis through its center. Point A is located on its rim and point B is located exactly one fifth of the way from the center toward the rim. What is the ratio of the angular velocity 𝜔_A to that of 𝜔_B, and the tangential velocity v_A to that of v_B?

(a) the angular velocity 𝜔_A to that of 𝜔_B

𝜔A/𝜔B= 

(b) the tangential velocity v_A to that of v_B

v_A

vB = 

The thickness of each plate is L1 = L2 =3 x 10-3

and metal plate 1 is at 100oC while plate 2 at

0oC. The surface A of metal plate 1 has dimensions 4cm x 2cm. Given that the thermal

conductivity of metal plate 1 is 48.1W/m.K and that of plate 2 is 68.2W/m.K, what is the

temperature of the soldered interface if there is a steady flow of heat from metal plate 1 to

plate2?

41.4oC