Understand the Acceleration Due to Gravity Formula and More!

A bicycle wheel has an initial angular velocity of 1.50 rad/s. (a) If its angular acceleration is constant and equal to ${\displaystyle 0.200ra\frac{d}{s^2}}$, what is its angular velocit at t=2.50 s? (b) Through what angle has the wheel turned between t = 0 and t = 2.50 s?

The best leaper in the animal kingdom is the puma, which can jump to a height of 3.7 m when leaving the ground at an angle of ${\displaystyle {45}^{\circ }}$. With what speed must the animal leave the ground to reach that height?

The wave function for a traveling wave on a taut string is (in SI units)(a) What are the speed and direction of travel of the wave? (b) What is the vertical position of an element of the string at t = 0, x = 0.100 m? What are (c) the wavelength and (d) the frequency of the wave? (e) What is the maximum transverse speed of an element of the string? ${\displaystyle y(x,t)=\left(0.350m\right)\sin (10\pi -3\pi x+\frac{\pi }{4})}$

A car is stopped at a traffic light. It then travels along a straight road such that its distance from the light is given by ${\displaystyle x\left(t\right)=b{t}^2-c{t}^3}$ , where ${\displaystyle b=2.40\frac{m}{s^2}}$ and ${\displaystyle c=0.120\frac{m}{s^3}}$ (a) Calculate the average velocity of the car for the time interval t = 0 to t = 10.0 s. (b) Calculate the instantaneous velocity of the car at t=0, t = 5.0 s, and t = 10.0 s. (c) How long after starting from rest is the car again at rest?

A boat is pulled into a dock by means of a winch 12 feet above the deck of the boat. 
(a) The winch pulls in rope at a rate of 4 feet per second. Determine the speed of the boat when there is 13 feet of rope out. What happens to the speed of the boat as it gets closer to the dock? 
(b) Suppose the boat is moving at a cons tant rate of 4 feet per second. Determine the speed at which the winch pulls in rope when the re is a tota l of 13 feet of rope out. What happens to the speed at which the winc h pulls in rope as the boat gets closer to the dock ?

Point charges ${\displaystyle q1=50\mu C}$ and ${\displaystyle q2=-25\mu C}$ are placed 1.0 m apart. What is the force on a third charge ${\displaystyle q3=20\mu C}$ placed midway between q1 and q2?

A helicopter carrying dr. evil takes off with a constant upward acceleration of ${\displaystyle 5.0\frac{m}{s^2}}$. Secret agent austin powers jumps on just as the helicopter lifts off the ground. Afterthe two men struggle for 10.0 s, powers shuts off the engineand steps out of the helicopter. Assume that the helicopter is infree fall after its engine is shut off and ignore effects of airresistance. 
a) What is the max height above ground reached by the helicopter? 
b) Powers deploys a jet pack strapped on his back 7.0s after leaving the helicopter, and then he has a constant downward acceleration with magnitude 2.0 m/s2. how far is powers above the ground when the helicopter crashes into the ground.

A floating ice block is pushed through a displacement d=(15m)i-(12m)j along a straight embankment by rushing water, which exerts a force F=(210N)i-(150N)j on the block. How much work does theforce do on the block during the displacement?

The initial velocity of a car, vi, is 45 km/h in the positivex direction. The final velocity of the car, vf, is 66 km/h indirection that points 75 degrees above the positive x axis. 
a) sketch the vectors -vi, vf and change in v. (b) findthe magnitude and direction in change of velocity. 
For b..my answer was -37.93 km/h and -88.41 degrees for direction.

You are on the roof of the physics building, 46.0 m above the ground. Your physics professor, who is 1.80 tall, is walking along side the building at a constant speed of 1.20 m/s. If you wish to drop an egg on your professor's head, how far from the building should the professor be when you release the egg? Assume that the egg is in free fall.Take the free fall acceleration to be ${\displaystyle 9.80\frac{m}{s^2}}$

An alpha particle (a He nucleus, containing two protons and two neutrons and having a mass of ${\displaystyle 6.64\cdot {10}^{-27}}$ kg) traveling horizontally at 35.6 km/s enters a uniform, vertical, 1.10 T magnetic field. 
A) What is the diameter of the path followed by this alpha particle? 
B) What effect does the magnetic field have on the speed of the particle? 
C) What are the magnitude of the acceleration of the alpha particle while it is in the magnetic field? 
D) What are the direction of the acceleration of the alpha particle while it is in the magnetic field?

If the coefficient of static friction between your coffeecup and the horizontal dashboard of your car is, how fast can you drive on a horizontal roadwayaround a right turn radius of 30.0 m before the cup starts toslide? If you go too fast, in what direction will the cupslide relative to the dashboard?

An airplane propeller is 2.08 m in length (from tip to tip) and has a mass of 117 kg. When the airpline's engine is first started, it applies a constant torque of ${\displaystyle 1950N\cdot m}$ to the propeller, which starts from rest.
a) What is the angular acceleration of the propeller? Model the propeller as a slender rod.
b) What is the propeller's angular speed after making 5.00 revolutions?
c) How much work is done by the engine during the first 5.00 revolutions?
e) What is the instantaneous power output of the motor at the instant that the propeller has turne through 5.00 revolutions?

The rotor (flywheel) of a toy gyroscope hasmass 0.140 kg. Its moment of inertia about its axis is . The mass of the frame is 0.0250 kg. The gyroscopeis supported on a single pivot javascript:void(0); with its center of mass a horizontaldistance of 4.00 cm from the pivot. The gyroscope is precessing ina horizontal plane at the rate of one revolution in 2.20 s. Find the upward force exerted by thepivot. Find the angular speed with which the rotoris spinning about its axis, expressed in rev/min. Comments

A rocket is launched at an angle of 53 degrees above the horizontal with an initial speed of 100 m/s. The rocket moves for 3.00 s a long its initial line of motion with an acceleration of 30.0 m/s/s. At this time, its engines fail and the rocket proceeds to move as a projectile. Find: 
a) the maximum altitude reached by the rocket 
b) its total time of flight 
c) its horizontal range.

A skier of mass 70 kg is pulled up a slope by a motor driven cable. (a) How much work is required to pull him 60m up a 30 degree slope (assumed frictionless) at a constant speed of 2.0 m/s ?(b) What power must a motor have to perform this task?

A chandelier with mass m is attached to the ceiling of a large concert hall by two cables.Because the ceiling is covered with intricate architectur al decorations (not indicated in the figure, which uses a humbler depiction), the workers who hung the chandelier couldn't attach the cables to the ceiling directly above the chandelier. Instead, they attached the cables to the ceiling near the walls. Cable 1 has tension ${\displaystyle T_1}$ and makes an angle of ${\displaystyle {\theta }_1}$ with the ceiling. Cable 2 has tension ${\displaystyle T_2}$ and makes an angle of ${\displaystyle {\theta }_2}$ with the ceiling.
Find an expression for ${\displaystyle T_1}$, the tension in cable 1, that does not depend on ${\displaystyle T_2}$.
Express your answer in terms of someor all of the variables m,${\displaystyle {\theta }_1}$, and ${\displaystyle {\theta }_2}$, as well as the magnitude of the acceleration due to gravity g.

A block is hung by a string from inside the roof of avan. When the van goes straight ahead at a speed of 24 m/s,the block hangs vertically down. But when the van maintains this same speed around an unbanked curve (radius = 175m) the block swings toward the outside of the curve, then the string makes an angle theta with the vertical. Find theta.

A 7.00- kg bowling ball moves at 3.00 m/s. How fast must a 2.45- g Ping Pong ball move so that the two balls have the same kinetic energy?

A golfer hits a golf ball at an angle of 25 degrees to the ground. If the golf ball covers a horizontal distance of 301. 5 m, what is the ball's maximum height? (Hint: at the top of its flight, the ball's vertical velocity component will be zero.)