A bike with tires of radius 0.330 m speeds up from rest to 5.33 m/s in 6.27 s. What is the angular acceleration of the tires?

1 answer:

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The angular acceleration of a bike with tires of radius 0.330 m speeds up from rest to 5.33 m/s in 6.27 s will be 2. 57 rad/s²

<h3>What is angular acceleration?</h3>

Angular acceleration can be defined as the time it takes for a change in angular velocity. It is denoted as 'α' with a unit of rads/s²

It is expressed thus;

α= Δω ÷ Δt

Where α = angular acceleration

Δw = change in angular velocity = velocity ÷ radius

Δ t = change in time

<h3>How to calculate the angular acceleration</h3>

Using the formula:

α= Δω ÷ Δt

v = 5. 33m/s, r = 0. 33m and t = 6.27s

Substitute the values to get the angular velocity

Δw = v÷ r = 5. 33 ÷ 0.330 = 16. 15 m/s

Substitute the value of Δw into the equation

α= Δω ÷ Δt = 16. 15 ÷ 6. 27 = 2. 57 rad/s²

Therefore, the angular acceleration of a bike with tires radius of 0. 330m, speed of 5. 33mls in 6. 27s is 2. 57 rad/s²

Learn more about angular acceleration here:

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A 400.0-m-wide river flows from west to east at 30.0 m/min. Your boat moves at 100.0 m/min relative to the water no matter which

Ratling [72]

Answer:

a. boat would drift towards a NE direction

b. 104.4m/min * t

c. false

d. point downstream of c, -79.19 deg NE

e. 3.898mins

f. 389.8m

Explanation:

a. downstream is a location with respect to the direction of the flow of the river, in this case from west to east. the boat would drift towards the NE direction due to the direction of water current.

b. lets say it takes time t to travel across the river, the resultant speed of boat would be given as Rs= sqrt ( 100/min^2 + 30m/mins^2) = 104.4m/mins

distance traveled would be 104.4 *t

c. false, the direction of boat wouldnt remain perpendicular the entire crossing but would drift toward the NE bearing provided the driver doesnt change or steer the boat.

d. a. taking the definition of downstream in question (a), your boat would land at a point x downstream to c

b. to land at c boat must be inclined at an angle of -79.19 deg NE, given by using the width of river and the distance of b to c.

cosФ= 75/ 400

Ф= 79.19°NE to get to c you must position boat at an angle of -79.19 deg from your initial bearing.

e. speed = distance/ time, time = distance / speed.

aiming toward point c, speed of boat is the resultant speed of boat with respect to the speed of water, using Pythagoras also

speed= $\sqrt{ 100^{2} + 30^{2} }$ = 104m/mins