Problem 5:Case 1:A DJ starts up her phonograph player. The turntable accelerates uniformly from rest, and takest₁=10.2seconds to get up to its full speed off₁= 78 revolutions per minute. Case 2:The DJ then changes the speed of the turntable fromf₁= 78 tof₂= 120 revolutions per minute. She notices that the turntable rotates exactlyn₂=14times while accelerating uniformly. Randomized Variables

t₁=10.2seconds n₂=14times

part (b)How many revolutions does the turntable make while accelerating in Case 1? n₁ =

Part (c)Calculate the magnitude of the angular acceleration of the turntable in Case 1, in radians/second². ₁ =

Part (d)Calculate the magnitude of the angular acceleration of the turntable (in radians/second²) while increasing to 120 RPM (Case 2). ₂ =

Part (e)How long (in seconds) does it take for the turntable to go from f₁ = 78 to f₂ = 120 RPM? t₂ =

Problem 6:At its lowest setting a centrifuge rotates with an angular speed of₁=350rad/s. When it is switched to the next higher setting it takest=13s to uniformly accelerate to its final angular speed₂=750rad/s.

Part (a)Calculate the angular acceleration of the centrifuge ₁ in rad/s² over the time interval t. ₁ =

art (b)Calculate the total angular displacement (in radians) of the centrifuge, , as it accelerates from the initial to the final speed. =

Problem 7:During a very quick stop, a car decelerates at6.2m/s². Assume the forward motion of the car corresponds to a positive direction for the rotation of the tires (and that they do not slip on the pavement). Randomized Variablesa_t=6.2m/s² r=0.29m ₀=92rad/s

Part (a)What is the angular acceleration of its tires in rad/s², assuming they have a radius of 0.29 m and do not slip on the pavement? =

Part (c)How long does the car take to stop completely in seconds? t=

Part (d)What distance does the car travel in this time in meters? x=

Part (e)What was the car's initial speed in m/s? v₀ =

Problem 9:It takes a timet=0.68s for a record to revolve on a record player once. A particular point on the record moves past the needle at a speed ofv_n=0.96m/s. Randomized Variablest=0.68s v_n=0.96m/s

Part (a)What is the radius at which the needle is in contact with the record in m? r_n =

Part (b)What is the tangential speed v₂ of a point on the record that is at r₂ = 0.05 m in m/s? v₂ =

Problem 16:A common carnival ride, called agravitron, is a large cylinder in which people stand against the wall of the ride as it rotates. At a certain point the floor of the cylinder lowers and the people are surprised that they don't slide down. Suppose the radius of the cylinder isr=19m, and the friction between the wall and their clothes is_s=0.69. Consider the tangential speedvof the ride's occupants as the cylinder spins.

Part (a)What is the minimum speed, in meters per second, that the cylinder must make a person move at to ensure they will "stick" to the wall? v_min =

Part (b)What is the frequency f in revolutions per minute of the carnival ride when it has reached the minimum speed to "stick" someone to the wall? f =

Problem 18:At takeoff, a commercial jet has a speed of74m/s. Its tires have a diameter of0.88m.

Part (a)At how many rev/min are the tires rotating? f =

Part (b)What is the centripetal acceleration at the edge of the tire in m/s²? a_c =

Part (c)With what force must a determined 1.15 10^-15 kg bacterium cling to the rim in N? F =

Part (d)Take the ratio of this force to the bacterium's weight. F/W =

Problem 19:A given highway turn has a95km/h speed limit and a radius of curvature of1.05km.

What banking angle (in degrees) will prevent cars from sliding off the road, assuming everyone travels at the speed limit and there is no friction present? =